{"id":4878,"date":"2021-08-31T17:47:18","date_gmt":"2021-08-31T17:47:18","guid":{"rendered":"https:\/\/mathemerize.com\/?p=4878"},"modified":"2021-09-11T18:41:08","modified_gmt":"2021-09-11T13:11:08","slug":"equality-of-matrices","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/equality-of-matrices\/","title":{"rendered":"Equality of Matrices Definition with Examples"},"content":{"rendered":"

Here you will learn equality of matrices definition with examples.<\/p>\n

Let’s begin –<\/p>\n

Equality of Matrices<\/h2>\n

Definition :\u00a0<\/strong>Two matrice A = \\([a_{ij}]_{m\\times n}\\) and B = \\([b_{ij}]_{r\\times s}\\) are equal if<\/p>\n

\n

(i) m = r i.e. the number of rows in A equals the number of rows in B.<\/p>\n

(ii) n = s i.e the number of columns in A equals the number of columns in B.<\/p>\n

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

If two matrices A and B are equal, we write A = B, otherwise we write A \\(\\ne\\) B.<\/p>\n

The matrices A = \\(\\begin{bmatrix} 3 & 2 & 1 \\\\ x &\u00a0 y & 5 \\\\ 1 & -1 &\u00a0 4\u00a0 \\end{bmatrix}\\) and B = \\(\\begin{bmatrix} 3 & 2 & 1 \\\\ -1 &\u00a0 0 & 5 \\\\ -1 & -1 &\u00a0 z\u00a0 \\end{bmatrix}\\) are equal if x = -1, y = 0 and z = 4.<\/p>\n

Matrices \\(\\begin{bmatrix} 0 & 0\u00a0 \\\\ 0 &\u00a0 0\u00a0 \\end{bmatrix}\\) and \\(\\begin{bmatrix} 0 & 0\u00a0 & 0 \\\\ 0 &\u00a0 0 & 0\u00a0 \\end{bmatrix}\\) are not equal, because their orders are not same.<\/p>\n\n\n

Example : <\/span>Find the value of x, y, z and w which satisfy the matrix equation, \\(\\begin{bmatrix} x – y & 2x + z  \\\\ 2x – y &  3z+ w \\end{bmatrix}\\) = \\(\\begin{bmatrix} -1 & 5  \\\\ 0 &  13 \\end{bmatrix}\\)<\/p>\n

Solution : <\/span>Since the corresponding elements of two equal matrices are equal. Therefore,

\\(\\begin{bmatrix} x – y & 2x + z  \\\\ 2x – y &  3z+ w \\end{bmatrix}\\) = \\(\\begin{bmatrix} -1 & 5  \\\\ 0 &  13 \\end{bmatrix}\\)

\n\\(\\implies\\) x – y = -1, 2x + z = 5, 2x – y = 0, 3z + w = 13

\nSolving the equation x – y = -1 and 2x- y = 0 as simultaneous linear equations, we get x = 1 and y = 2.

\nNow, putting x = 1 in 2x + z = 5, we get z = 3. Substituting z = 3 in 3z + w = 13, we obtain w = 4

\nThus, x = 1, y = 2, z = 3 and w = 4

<\/p>\n\n\n\n

\n
Next – Addition of Matrices \u2013 Properties & Examples<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Different Types of Matrices<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn equality of matrices definition with examples. Let’s begin – Equality of Matrices Definition :\u00a0Two matrice A = \\([a_{ij}]_{m\\times n}\\) and B = \\([b_{ij}]_{r\\times s}\\) are equal if (i) m = r i.e. the number of rows in A equals the number of rows in B. (ii) n = s i.e the …<\/p>\n

Equality of Matrices Definition with 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":[],"yoast_head":"\nEquality of Matrices Definition with Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn equality of matrices definition 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\/equality-of-matrices\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Equality of Matrices Definition with Examples - 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