{"id":4883,"date":"2021-08-31T12:57:40","date_gmt":"2021-08-31T12:57:40","guid":{"rendered":"https:\/\/mathemerize.com\/?p=4883"},"modified":"2022-01-16T17:00:03","modified_gmt":"2022-01-16T11:30:03","slug":"scalar-multiplication-with-matrices","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/scalar-multiplication-with-matrices\/","title":{"rendered":"Scalar Multiplication with Matrices – Properties and Examples"},"content":{"rendered":"

Here you will learn scalar multiplication with matrices (multiplicaition of a matrix by a scalar ) and properties of scalar mutiplication.<\/p>\n

Let’s begin – <\/p>\n

Scalar Multiplication with Matrices<\/h2>\n

Definition : <\/strong>Let \\([a_{ij}]\\) be an \\(m\\times n\\) matrix and k be any number called a scalar. Then the matrix obtained by mutiplying every element of A by k is called the scalar multiple of A by k and is denoted by kA.<\/p>\n

Thus, <\/p>\n

\n

kA = \\([ka_{ij}]_{m\\times n}\\)<\/p>\n<\/blockquote>\n

Example : <\/span><\/strong>if A = \\(\\begin{bmatrix} 1 & 2 & 5 \\\\ -2 &  3 & 4 \\\\ 1 & 2 &  -1  \\end{bmatrix}\\), then 3A = \\(\\begin{bmatrix} 3 & 6 & 15 \\\\  -6 &  9 & 12 \\\\ 3 & 6 &  -3  \\end{bmatrix}\\)<\/p>\n

 <\/span><\/strong>if A = \\(\\begin{bmatrix} 6 & 2 & 3 \\\\ 2 &  3 & -2 \\\\ 2 & 4 &  1  \\end{bmatrix}\\), then \\(1\\over 2\\)A = \\(\\begin{bmatrix} 3 & 1 & 3\/2 \\\\  1 &  3\/2 & -1 \\\\ 1 & 2 &  1\/2  \\end{bmatrix}\\)<\/p>\n

Example : <\/span><\/strong> Let A = \\(\\begin{bmatrix} 1 & 5 & 7 & 3\\\\ -1 &  5 & 9 & 4 \\\\ -2 & 6 &  3 & -5  \\end{bmatrix}\\), then 2A = \\(\\begin{bmatrix} 2 & 10 & 14 & 6\\\\ -2 &  10 & 18 & 8 \\\\ -4 & 12 &  6 & -10  \\end{bmatrix}\\)<\/p>\n

and \\(1\\over 2\\)A = \\(\\begin{bmatrix} 1\/2 & 5\/2 & 7\/2 & 3\/2 \\\\ -1\/2 &  5\/2 & 9\/2 & 2 \\\\ -1 & 3 &  3\/2 & -5\/2 \\end{bmatrix}\\)<\/p>\n

Properties of scalar multiplication<\/strong><\/h4>\n

Various properties of scalar multiplication are stated below :<\/p>\n

If A = \\([a_{ij}]_{m\\times n}\\), B = \\([b_{ij}]_{m\\times n}\\) are two matrices and k and l are scalars, then<\/p>\n

(i) k (A + B) = k A + k B<\/p>\n

(ii) (k + l) A = k A + l A<\/p>\n

(iii)  (k l) A = k (l A) = l (k A)<\/p>\n

(iv) (-k) A = –  (k A) = k(-A)<\/p>\n

(v) 1 A = A<\/p>\n

(vi) (-1) A = -A <\/p>\n\n\n

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

Here you will learn scalar multiplication with matrices (multiplicaition of a matrix by a scalar ) and properties of scalar mutiplication. Let’s begin –  Scalar Multiplication with Matrices Definition : Let \\([a_{ij}]\\) be an \\(m\\times n\\) matrix and k be any number called a scalar. Then the matrix obtained by mutiplying every element of A by …<\/p>\n

Scalar Multiplication with 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":[486,485,492,491],"yoast_head":"\nScalar Multiplication with Matrices - Properties and Examples<\/title>\n<meta name=\"description\" content=\"Learn scalar multiplication with matrices (multiplicaition of a matrix by a scalar ) and properties of scalar mutiplication.\" \/>\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\/scalar-multiplication-with-matrices\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Scalar Multiplication with Matrices - 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