{"id":4881,"date":"2021-08-31T12:25:15","date_gmt":"2021-08-31T12:25:15","guid":{"rendered":"https:\/\/mathemerize.com\/?p=4881"},"modified":"2022-01-16T17:00:19","modified_gmt":"2022-01-16T11:30:19","slug":"addition-of-matrices","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/addition-of-matrices\/","title":{"rendered":"Addition of Matrices – Properties and Examples"},"content":{"rendered":"

Here you will learn how to add matrix and properties of addition of matrices with examples.<\/p>\n

Let’s begin –<\/p>\n

Addition of Matrices<\/h2>\n

Let A, B be two matrices, each of order \\(m \\times n\\). Then their sum A + B is a matrix of order \\(m \\times n\\) and is obtained by adding the correspoding elements of A and B.<\/p>\n

Thus, if A = \\([a_{ij}]_{m\\times n}\\) and B = \\([b_{ij}]_{m\\times n}\\) are two matrices of the same order, their sum A + B is defined to be the matrix of order \\(m\\times n\\) such that<\/p>\n

\\((A + B)_{ij}\\) = \\(a_{ij}\\) + \\(b_{ij}\\) for i = 1, 2, ……. , m and  j = 1, 2, ……. n<\/p>\n

Note<\/strong> : The sum of two matrices is defined by only when they are of the same order.<\/p>\n

Example :<\/strong> If A = \\(\\begin{bmatrix} 1 & 2 & 3 \\\\ 4 &  5 & 6  \\end{bmatrix}\\), B = \\(\\begin{bmatrix} 6 & 5 & 4 \\\\ 3 &  2 & 1  \\end{bmatrix}\\), then<\/p>\n

A + B = \\(\\begin{bmatrix} 1 + 6 & 2 + 5 & 3 + 4 \\\\ 4 + 3 &  5 + 2 & 6 + 1  \\end{bmatrix}\\) = \\(\\begin{bmatrix} 7 & 7 & 7 \\\\ 7 &  7 & 7  \\end{bmatrix}\\)<\/p>\n

If A = \\(\\begin{bmatrix} 1 & 2 & 3 \\\\ 4 &  5 & 6  \\end{bmatrix}\\), B = \\(\\begin{bmatrix} -1 & 2 & 1 \\\\ 3 &  2 & 1 \\\\ 2 & 5 & -2 \\end{bmatrix}\\), then A + B is not defined, because A and B are not of the same order.<\/p>\n

Properties of Matrix Addition<\/h2>\n

(a) Commutativity<\/strong> :  If A and B are two \\(m\\times n\\) matrices, then A + B = B + A. i.e. matrix addition is commutative.<\/p>\n

(b) Associativity<\/strong> : If A, B, C are three matrices of the same order, then (A + B) + C = A + (B + C) i.e. matrix addition is associative.<\/p>\n

(c) Existence of Identity<\/strong> : The null matrix is the identity element for matrix addition.<\/p>\n

(d) Existence of Inverse<\/strong> : for every matrix A = \\([a_{ij}]_{m\\times n}\\) there exist a matrix \\([-a_{ij}]_{m\\times n}\\), denoted by -A, such that A + (-A) = O = (-A) + A<\/p>\n

(e) Cancellation Laws<\/strong> : If A, B, C are matrices of the same order, then<\/p>\n

A + B = A + C \\(\\implies\\) B = C      <\/p>\n

and, B + A = C + A \\(\\implies\\) B = C<\/p>\n\n\n

\n
Next – Scalar Multiplication with Matrices \u2013 Properties & Examples<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Equality of Matrices<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn how to add matrix and properties of addition of matrices with examples. Let’s begin – Addition of Matrices Let A, B be two matrices, each of order \\(m \\times n\\). Then their sum A + B is a matrix of order \\(m \\times n\\) and is obtained by adding the correspoding …<\/p>\n

Addition of Matrices – Properties and Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[34],"tags":[493,494,495],"yoast_head":"\nAddition of Matrices - Properties and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn how to add matrix and properties of addition of matrices with examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/addition-of-matrices\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Addition of Matrices - 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