{"id":33350,"date":"2023-08-23T15:46:00","date_gmt":"2023-08-23T15:46:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=33350"},"modified":"2023-08-24T04:48:07","modified_gmt":"2023-08-24T04:48:07","slug":"row-matrix-definition-formula-properties-facts-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/row-matrix","title":{"rendered":"Row Matrix: Definition, Formula, Properties, Facts, Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-fc0e633c-c6c7-43ea-b552-cb53ba46e381\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/row-matrix#0-what-is-a-row-matrix>What Is a Row Matrix?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/row-matrix#4-properties-of-row-matrix>Properties of Row Matrix<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/row-matrix#6-types-of-matrices>Types of Matrices<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/row-matrix#9-solved-examples-on-row-matrix>Solved Examples on Row Matrix<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/row-matrix#10-practice-problems-on-row-matrix>Practice Problems on Row Matrix<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/row-matrix#11-frequently-asked-questions-about-row-matrix>Frequently Asked Questions about Row Matrix<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-a-row-matrix\">What Is a Row Matrix?<\/h2>\n\n\n\n<p><strong>A row matrix is a type of a matrix that has only one row.&nbsp;<\/strong><\/p>\n\n\n\n<p>The total number of columns in a row matrix is the total number of elements that make up the single <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/row\">row<\/a>.&nbsp;<\/p>\n\n\n\n<p>The row matrix is not a square matrix as the number of rows is not equal to the number of columns. Thus, we cannot find the determinant of a row matrix.<\/p>\n\n\n\n<p><strong>Examples of a row matrix:&nbsp;<\/strong><\/p>\n\n\n\n<p>A<sub>1 x 3<\/sub> $= \\left[7\u00a0 \\;5\u00a0 \\;6\\right]$<\/p>\n\n\n\n<p>B<sub>1 x 4<\/sub> $= \\left[10\u00a0\\; 22\u00a0\\; 63\u00a0\\; 12\\right]$<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-rows-and-columns\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_foundation_count_row_col_pt.png\" alt=\"Count Rows and Columns Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count Rows and Columns Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-the-number-of-rows-and-columns\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_facts_count_rowcol_pt.png\" alt=\"Identify the Number of Rows and Columns Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify the Number of Rows and Columns Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/understand-rows-in-an-array\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_facts_journey_2_gm.png\" alt=\"Understand Rows in an Array Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Understand Rows in an Array Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-definition-of-row-matrix\">Definition of Row Matrix<\/h2>\n\n\n\n<p>A row matrix is a matrix of an order $1 \\times n$, where n is the number of columns.\u00a0<\/p>\n\n\n\n<p>A row matrix can be expressed in mathematical form as:<\/p>\n\n\n\n<p>A = [a\u2081\u2081\u00a0 a\u2081\u2082\u00a0 a\u2081\u2083 &#8230;&#8230;. a\u2081\u2099]<sub>1 x <\/sub><sub>n<\/sub><\/p>\n\n\n\n<p>where,<\/p>\n\n\n\n<p>a\u2081\u2081 , a\u2081\u2082 , a\u2081\u2083 ,&#8230;&#8230;., a\u2081\u2099 are the elements&nbsp;<\/p>\n\n\n\n<p>$n =$ number of columns\u00a0<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/number-of-rows-and-columns\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/number-of-rows-and-columns.jpeg\" alt=\"Number of Rows and Columns Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/rows-and-columns-in-an-array\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/rows-and-columns-in-an-array.jpeg\" alt=\"Rows and Columns in an Array Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/rows-and-columns\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/rows-and-columns.jpeg\" alt=\"Rows and Columns Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-order-of-a-row-matrix\">Order of a Row Matrix<\/h2>\n\n\n\n<p>The order of a row matrix is $1 \\times n$, where 1 represents the number of rows and n is the number of columns.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"285\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/order-of-a-row-matrix.png\" alt=\"Order of a row matrix\" class=\"wp-image-33359\" title=\"Order of a row matrix\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/order-of-a-row-matrix.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/order-of-a-row-matrix-300x138.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-transpose-of-a-row-matrix\">Transpose of a Row Matrix<\/h2>\n\n\n\n<p>The transpose of a row matrix of order $1 \\times n$ is a column matrix of order $n \\times 1$. It is obtained by interchanging the row by a column. Transpose of a matrix A is denoted by A\u2019 or A<sup>T<\/sup>.<\/p>\n\n\n\n<p><strong>Example: <\/strong>The transpose of the row matrix $A = \\left[ 7\u00a0 \\;6\u00a0\\;-\\;9\\right]$ is\u00a0<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/row-equation-fig-1.png\" alt=\"\" class=\"wp-image-33363\" style=\"width:79px;height:98px\" width=\"79\" height=\"98\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-properties-of-row-matrix\">Properties of Row Matrix<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>There is only one row in a row matrix.<\/li>\n\n\n\n<li>The total number of columns in a matrix equals the total number of elements in the row.<\/li>\n\n\n\n<li>A row matrix is a type of a rectangular matrix.<\/li>\n\n\n\n<li>A transpose of a row matrix with order $1 \\times n$ is a column matrix with order $n \\times 1$.<\/li>\n\n\n\n<li>The row matrix can only be added to (or subtracted from) another row matrix with the same order.<\/li>\n\n\n\n<li>A <strong>row matrix<\/strong> with order $1 \\times n$ can only be multiplied by a column matrix of order $n \\times 1$.<\/li>\n\n\n\n<li>A singleton matrix (matrix of order $1 \\times 1$ which has only one element) is produced when a row matrix and a column matrix are multiplied.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-row-matrix-operations\">Row Matrix Operations<\/h2>\n\n\n\n<p>We can perform simple arithmetic operations across a row matrix, such as addition, subtraction, multiplication, and division.&nbsp;<\/p>\n\n\n\n<p>We can only add or subtract row matrices of the same order. To add\/subtract two or more matrices, we add\/subtract the corresponding elements.&nbsp;&nbsp;<\/p>\n\n\n\n<p><strong>Example:&nbsp;<\/strong><\/p>\n\n\n\n<p>$A = \\left[3\u00a0 9\u00a0 8\\right]$ and $B = \\left[5\u00a0\\; 1\u00a0\\; 7\\right]$<\/p>\n\n\n\n<p>$A + B = \\left[3 + 5 \u00a0\\; 9 + 1 \u00a0\\; 8 + 7\\right] = \\left[8 \u00a0\\; 10 \u00a0 \\;15\\right]$<\/p>\n\n\n\n<p>$A \\;-\\; B = \\left[3 \\;-\\; 5 \\; 9 \\;-\\; 1 \\; 8 \\;-\\; 7\\right] = \\left[\\;-\\;2 \u00a0\\; 8 \u00a0\\; 1\\right]$<\/p>\n\n\n\n<p>We can multiply a row matrix with a column matrix. We can multiply a row matrix of order $1 \\times n$ only with a column matrix of order $n \\times 1$. The result of the multiplication of a row and a column matrix is a singleton matrix.\u00a0<\/p>\n\n\n\n<p><strong>Example:&nbsp;<\/strong><\/p>\n\n\n\n<p>Let us consider matrix $A = \\left[2\u00a0\\; 5\u00a0 \\;3\\right]$ and\u00a0\u00a0<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/row-equation-fig-2-edited.png\" alt=\"\" class=\"wp-image-33365\" style=\"width:69px;height:85px\" width=\"69\" height=\"85\"\/><\/figure>\n\n\n\n<p>matrix B =<\/p>\n\n\n\n<p>$A \\times B = \\left[(2 \\times 7) + (5 \\times 6) + (3\\times -9)\\right]$<\/p>\n\n\n\n<p>$A \\times B = \\left[14 + 30 \\;-\\; 27\\right]$<\/p>\n\n\n\n<p>$A \\times B = \\left[44 \\;-\\; 27\\right]$<\/p>\n\n\n\n<p>$A \\times B = \\left[17\\right]$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-types-of-matrices\">Types of Matrices<\/h2>\n\n\n\n<p>There are ten different kinds of matrices. They are as follows:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Row matrix:<\/strong> A matrix that has only one row.<\/li>\n\n\n\n<li><strong>Column matrix:<\/strong> A matrix which contains only one column.<\/li>\n\n\n\n<li><strong>Diagonal matrix:<\/strong> A square matrix that has 0 as the element on the leading diagonals.<\/li>\n\n\n\n<li><strong>Scalar matrix:<\/strong> This kind of matrix has the same elements on the diagonal.<\/li>\n\n\n\n<li><strong>Square matrix:<\/strong> This type of matrix has the same number of rows and columns.<\/li>\n\n\n\n<li><strong>Identity matrix:<\/strong> It is also known as a unit matrix. A matrix with all the diagonal elements equal to 1.<\/li>\n\n\n\n<li><strong>Zero matrix:<\/strong> All the elements of this matrix are zero. It is also called a null matrix.<\/li>\n\n\n\n<li><strong>Triangular matrix:<\/strong> In this matrix, all the elements above or below the matrix leading diagonal are zero. There are two types of triangular matrix: upper triangular matrix and lower triangular matrix.<\/li>\n\n\n\n<li><strong>Symmetric matrix:<\/strong> A square matrix [a\u1d62\u2c7c] is a symmetric matrix when $a_{ij} = a_{ji}$.<\/li>\n\n\n\n<li><strong>Skew symmetric matrix: <\/strong>A skew-symmetric matrix is the kind of square matrix [a\u1d62\u2c7c] when $a_{ij} = \\;-\\;a_{ji}$. The elements of the leading diagonal of this matrix are 0.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-facts-about-row-matrices\">Facts about Row Matrices<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>The division operation is not possible for a row matrix because the inverse of this type of matrix does not exist.<\/li>\n\n\n\n<li>A row matrix is also called a row vector in linear algebra.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about row matrices, their properties and also discussed operations on row matrices. Let\u2019s use the concepts we learned to solve a few examples and practice problems.&nbsp;&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-solved-examples-on-row-matrix\">Solved Examples on Row Matrix<\/h2>\n\n\n\n<p><strong>1. Find the sum of the row matrices <\/strong>$A = \\left[4\u00a0\\; 10\u00a0\\; 11\\right]$<strong> and B <\/strong>$= \\left[6\\;\u00a0 5\u00a0\\; 20\\right]$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution: <\/strong>The given matrices are<\/p>\n\n\n\n<p>$A = \\left[4\u00a0 \\;10\\;\u00a0 11\\right]$\u00a0<\/p>\n\n\n\n<p>$B = \\left[6\u00a0\\; 5\u00a0\\; 20\\right]$<\/p>\n\n\n\n<p>$A + B = \\left[4\\;\u00a0 10\u00a0 \\;11] + [6\u00a0 \\;5\u00a0 \\;20\\right]$<\/p>\n\n\n\n<p>$A + B = \\left[4 + 6 \\;\u00a0 10 + 5 \\;\u00a0 11 + 20\\right]$<\/p>\n\n\n\n<p>$A + B = \\left[10\\;\u00a0 15\u00a0 \\;31\\right]$<\/p>\n\n\n\n<p>Therefore, the resultant matrix $A + B = \\left[10\u00a0\\; 15\\;\u00a0 31\\right]$.<\/p>\n\n\n\n<p><strong>2. Subtract matrix <\/strong>$B = \\left[31\u00a0\\; 25\\;\u00a0 16\\right]$<strong> from matrix <\/strong>$A = \\left[47\u00a0\\; 25\u00a0\\; 34\\right]$<strong>.\u00a0<\/strong><\/p>\n\n\n\n<p><strong>Solution: <\/strong>The given matrices are:&nbsp;<\/p>\n\n\n\n<p>$B = \\left[31\u00a0\\; 25\u00a0\\; 16\\right]$<\/p>\n\n\n\n<p>$A = \\left[47\u00a0\\; 25\u00a0\\; 34\\right]$<\/p>\n\n\n\n<p>$A \\;-\\; B = \\left[47\u00a0 25\u00a0\\; 34\\right] \\;-\\; \\left[31\u00a0 \\;25\u00a0\\; 16\\right]$<\/p>\n\n\n\n<p>$A \\;-\\; B = \\left[47\\;-\\;31 \\; 25\\;-\\;25 \\; 31\\;-\\;16\\right]$<\/p>\n\n\n\n<p>$A \\;-; B = \\left[16\\;\u00a0 0\u00a0\\; 15\\right]$<\/p>\n\n\n\n<p>Therefore, the resultant matrix would be $A \\;-\\; B = \\left[16\\;\u00a0 0\u00a0 \\;15\\right]$<\/p>\n\n\n\n<p><strong>3. Find the product of the following matrices <\/strong>$A = \\left[2\u00a0\\; 6\u00a0 \\;7\u00a0 \\;-\\;5\\right]$<strong> and B =<\/strong> <img loading=\"lazy\" decoding=\"async\" width=\"45\" height=\"100\" class=\"wp-image-33366\" style=\"width: 45px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/rwo-equation-fig-3.png\" alt=\"\"><\/p>\n\n\n\n<p><strong>Solution: <\/strong>The given matrices are<\/p>\n\n\n\n<p>$A = \\left[2\u00a0\\; 6\u00a0 \\;7\u00a0 \\;-\\;5\\right]$\u00a0<\/p>\n\n\n\n<p>B = <img loading=\"lazy\" decoding=\"async\" width=\"45\" height=\"100\" class=\"wp-image-33367\" style=\"width: 45px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/row-equation-fig-4.png\" alt=\"\"><\/p>\n\n\n\n<p>$A \\times B =\u00a0 \\left[(2 \\times 3) + (\\;-\\;5 \\times 6) + (7 \\times 4) + (\\;-\\;5 \\times \\;-\\;1)\\right]$\u00a0<\/p>\n\n\n\n<p>$A \\times B =\u00a0 \\left[6 \\;-\\; 30 + 28 + 5\\right]$\u00a0<\/p>\n\n\n\n<p>$A \\times B = \\left[39 \\;-\\; 30\\right]$<\/p>\n\n\n\n<p>$A \\times B = \\left[9\\right]$<\/p>\n\n\n\n<p>Therefore, the product of the matrices is $A \\times B = \\left[9\\right]$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-practice-problems-on-row-matrix\">Practice Problems on Row Matrix<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Row Matrix: Definition, Formula, Properties, Facts, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">$M = \\left[15  \\;24 \\; 30 \\; 41\\right]$ and $N = \\left[20 \\; 37 \\; 28 \\; 11\\right]$. Find $M + N$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\left[30 \\; 62 \\; 58 \\; 52\\right]$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\left[35 \\; 61 \\; 58\\;  52\\right]$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\left[35 \\; 61 \\; 59  \\;55\\right]$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\left[36 \\; 61  \\;58 \\; 52\\right]$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\left[35 \\; 61 \\; 58\\;  52\\right]$<br\/>When we add matrix M and N, we get<br>\r\n$M + N = \\left[15 + 20  \\; 24 + 37  \\; 30 + 28 \\;  41 + 11\\right] = \\left[35 \\; 61 \\; 58  \\;52\\right]$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The order of the row matrix $C = \\left[6 \\; 2 \\; 1  \\;3\\right]$ is<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$4 \\times 4$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$6 \\times 1$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$4 \\times 1$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$1 \\times 4$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $1 \\times 4$<br\/>The matrix has a single row and 4 columns. Thus, the order of the matrix $C = \\left[6 \\; 2 \\; 1  \\;3\\right]$ is $1 \\times 4$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Addition of zero matrix of order $1 \\times 3$ and the matrix $\\left[1 \\; 2 \\; 3\\right]$ is<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\left[3 \\; 2 \\; 1\\right]$<\/div><div class=\"spq_answer_block\" data-value=\"1\">6<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\left[1 \\; 2 \\; 3\\right]$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\left[\\;-\\;1  \\;-\\;2  \\;-\\;3\\right]$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\left[1 \\; 2 \\; 3\\right]$<br\/>$\\left[1 \\; 2 \\; 3\\right] + \\left[0  \\;0  \\;0\\right] = \\left[1  \\;2  \\;3\\right]$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Row Matrix: Definition, Formula, Properties, Facts, Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Row Matrix: Definition, Formula, Properties, Facts, Examples\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"$$M = \\\\left[15  \\\\;24 \\\\; 30 \\\\; 41\\\\right]$$ and $$N = \\\\left[20 \\\\; 37 \\\\; 28 \\\\; 11\\\\right]$$. Find $$M + N$$.\",\n                    \"text\": \"$$M = \\\\left[15  \\\\;24 \\\\; 30 \\\\; 41\\\\right]$$ and $$N = \\\\left[20 \\\\; 37 \\\\; 28 \\\\; 11\\\\right]$$. Find $$M + N$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"When we add matrix M and N, we get<br>\r\n$$M + N = \\\\left[15 + 20  \\\\; 24 + 37  \\\\; 30 + 28 \\\\;  41 + 11\\\\right] = \\\\left[35 \\\\; 61 \\\\; 58  \\\\;52\\\\right]$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left[30 \\\\; 62 \\\\; 58 \\\\; 52\\\\right]$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"When we add matrix M and N, we get<br>\r\n$$M + N = \\\\left[15 + 20  \\\\; 24 + 37  \\\\; 30 + 28 \\\\;  41 + 11\\\\right] = \\\\left[35 \\\\; 61 \\\\; 58  \\\\;52\\\\right]$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left[35 \\\\; 61 \\\\; 59  \\\\;55\\\\right]$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"When we add matrix M and N, we get<br>\r\n$$M + N = \\\\left[15 + 20  \\\\; 24 + 37  \\\\; 30 + 28 \\\\;  41 + 11\\\\right] = \\\\left[35 \\\\; 61 \\\\; 58  \\\\;52\\\\right]$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left[36 \\\\; 61  \\\\;58 \\\\; 52\\\\right]$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"When we add matrix M and N, we get<br>\r\n$$M + N = \\\\left[15 + 20  \\\\; 24 + 37  \\\\; 30 + 28 \\\\;  41 + 11\\\\right] = \\\\left[35 \\\\; 61 \\\\; 58  \\\\;52\\\\right]$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\left[35 \\\\; 61 \\\\; 58\\\\;  52\\\\right]$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"When we add matrix M and N, we get<br>\r\n$$M + N = \\\\left[15 + 20  \\\\; 24 + 37  \\\\; 30 + 28 \\\\;  41 + 11\\\\right] = \\\\left[35 \\\\; 61 \\\\; 58  \\\\;52\\\\right]$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"When we add matrix M and N, we get<br>\r\n$$M + N = \\\\left[15 + 20  \\\\; 24 + 37  \\\\; 30 + 28 \\\\;  41 + 11\\\\right] = \\\\left[35 \\\\; 61 \\\\; 58  \\\\;52\\\\right]$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The order of the row matrix $$C = \\\\left[6 \\\\; 2 \\\\; 1  \\\\;3\\\\right]$$ is\",\n                    \"text\": \"The order of the row matrix $$C = \\\\left[6 \\\\; 2 \\\\; 1  \\\\;3\\\\right]$$ is\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The matrix has a single row and 4 columns. Thus, the order of the matrix $$C = \\\\left[6 \\\\; 2 \\\\; 1  \\\\;3\\\\right]$$ is $$1 \\\\times 4$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$4 \\\\times 4$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The matrix has a single row and 4 columns. Thus, the order of the matrix $$C = \\\\left[6 \\\\; 2 \\\\; 1  \\\\;3\\\\right]$$ is $$1 \\\\times 4$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$6 \\\\times 1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The matrix has a single row and 4 columns. Thus, the order of the matrix $$C = \\\\left[6 \\\\; 2 \\\\; 1  \\\\;3\\\\right]$$ is $$1 \\\\times 4$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$4 \\\\times 1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The matrix has a single row and 4 columns. Thus, the order of the matrix $$C = \\\\left[6 \\\\; 2 \\\\; 1  \\\\;3\\\\right]$$ is $$1 \\\\times 4$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$1 \\\\times 4$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The matrix has a single row and 4 columns. Thus, the order of the matrix $$C = \\\\left[6 \\\\; 2 \\\\; 1  \\\\;3\\\\right]$$ is $$1 \\\\times 4$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The matrix has a single row and 4 columns. Thus, the order of the matrix $$C = \\\\left[6 \\\\; 2 \\\\; 1  \\\\;3\\\\right]$$ is $$1 \\\\times 4$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Addition of zero matrix of order $$1 \\\\times 3$$ and the matrix $$\\\\left[1 \\\\; 2 \\\\; 3\\\\right]$$ is\",\n                    \"text\": \"Addition of zero matrix of order $$1 \\\\times 3$$ and the matrix $$\\\\left[1 \\\\; 2 \\\\; 3\\\\right]$$ is\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\left[1 \\\\; 2 \\\\; 3\\\\right] + \\\\left[0  \\\\;0  \\\\;0\\\\right] = \\\\left[1  \\\\;2  \\\\;3\\\\right]$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left[3 \\\\; 2 \\\\; 1\\\\right]$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\left[1 \\\\; 2 \\\\; 3\\\\right] + \\\\left[0  \\\\;0  \\\\;0\\\\right] = \\\\left[1  \\\\;2  \\\\;3\\\\right]$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\left[1 \\\\; 2 \\\\; 3\\\\right] + \\\\left[0  \\\\;0  \\\\;0\\\\right] = \\\\left[1  \\\\;2  \\\\;3\\\\right]$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\left[\\\\;-\\\\;1  \\\\;-\\\\;2  \\\\;-\\\\;3\\\\right]$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\left[1 \\\\; 2 \\\\; 3\\\\right] + \\\\left[0  \\\\;0  \\\\;0\\\\right] = \\\\left[1  \\\\;2  \\\\;3\\\\right]$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\left[1 \\\\; 2 \\\\; 3\\\\right]$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\left[1 \\\\; 2 \\\\; 3\\\\right] + \\\\left[0  \\\\;0  \\\\;0\\\\right] = \\\\left[1  \\\\;2  \\\\;3\\\\right]$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\left[1 \\\\; 2 \\\\; 3\\\\right] + \\\\left[0  \\\\;0  \\\\;0\\\\right] = \\\\left[1  \\\\;2  \\\\;3\\\\right]$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-frequently-asked-questions-about-row-matrix\">Frequently Asked Questions about Row Matrix<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-75dc6f2b-54de-43a9-9068-b0d284f08204\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-75dc6f2b-54de-43a9-9068-b0d284f08204\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-75dc6f2b-54de-43a9-9068-b0d284f08204\"><strong>What is a nonsingular matrix?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-75dc6f2b-54de-43a9-9068-b0d284f08204\">\n\n<p>A matrix whose determinant is non-zero is called a nonsingular matrix.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-75dc6f2b-54de-43a9-9068-b0d284f08204\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-75dc6f2b-54de-43a9-9068-b0d284f08204\"><strong>What is the difference between a column matrix and a row matrix?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-75dc6f2b-54de-43a9-9068-b0d284f08204\">\n\n<p>A row matrix can have only one column, while a column matrix can have multiple columns. The number of columns in a row matrix is equal to the number of elements in it, while the number of rows in a column matrix is the number of elements in it.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-75dc6f2b-54de-43a9-9068-b0d284f08204\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-75dc6f2b-54de-43a9-9068-b0d284f08204\"><strong>What is the formula of a row matrix?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-75dc6f2b-54de-43a9-9068-b0d284f08204\">\n\n<p>The order of a row matrix is 1n, where 1 is the number of rows that remains constant, and n is the number of columns.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-75dc6f2b-54de-43a9-9068-b0d284f08204\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-75dc6f2b-54de-43a9-9068-b0d284f08204\"><strong>Do row matrices have an inverse?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-75dc6f2b-54de-43a9-9068-b0d284f08204\">\n\n<p>Only a square matrix can have an inverse.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-75dc6f2b-54de-43a9-9068-b0d284f08204\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-75dc6f2b-54de-43a9-9068-b0d284f08204\"><strong>What are the three matrix row operations?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-75dc6f2b-54de-43a9-9068-b0d284f08204\">\n\n<ul class=\"wp-block-list\">\n<li>Row swapping (switching rows)<\/li>\n\n\n\n<li>Multiplying a row by a non-zero constant<\/li>\n\n\n\n<li>Adding rows<\/li>\n<\/ul>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is a Row Matrix? A row matrix is a type of a matrix that has only one row.&nbsp; The total number of columns in a row matrix is the total number of elements that make up the single row.&nbsp; The row matrix is not a square matrix as the number of rows is not &#8230; <a title=\"Row Matrix: Definition, Formula, Properties, Facts, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/row-matrix\" aria-label=\"More on Row Matrix: Definition, Formula, Properties, Facts, Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-33350","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33350","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=33350"}],"version-history":[{"count":9,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33350\/revisions"}],"predecessor-version":[{"id":33372,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33350\/revisions\/33372"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=33350"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=33350"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=33350"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}