{"id":4889,"date":"2021-08-31T17:51:33","date_gmt":"2021-08-31T17:51:33","guid":{"rendered":"https:\/\/mathemerize.com\/?p=4889"},"modified":"2021-08-31T17:57:51","modified_gmt":"2021-08-31T17:57:51","slug":"subtraction-of-matrices","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/subtraction-of-matrices\/","title":{"rendered":"Subtraction of Matrices with Examples"},"content":{"rendered":"
Here you will learn subtraction of matrices with examples.<\/p>\n
Let’s begin –<\/p>\n
Let two matrices A and B of the same order, the subtraction of matrix B from matrix A is denoted by A – B and is defined as A – B = A + (-B).<\/p>\n
Note<\/strong> : If matrices are not of same order then subtraction of matrix is not possible.<\/p>\n If A = \\(\\begin{bmatrix} 2 & 1 \\\\ 0 & 2 \\end{bmatrix}\\) and B = \\(\\begin{bmatrix} 1 & 0 \\\\ 1 & 2 \\end{bmatrix}\\), then find A – B.<\/p>\n A – B = A + (-B) = \\(\\begin{bmatrix} 2 & 1 \\\\ 0 & 2 \\end{bmatrix}\\) – \\(\\begin{bmatrix} 1 & 0 \\\\ 1 & 2 \\end{bmatrix}\\)<\/p>\n = \\(\\begin{bmatrix} 1 & 1 \\\\ -1 & 0 \\end{bmatrix}\\)<\/p>\n If A = \\(\\begin{bmatrix} 2 & 3 & 4 \\\\ 0 & 4 & 6 \\\\ 5 & 8 & 9 \\end{bmatrix}\\) and B = \\(\\begin{bmatrix} 3 & 0 & 5 \\\\ 5 & 3 & 2 \\\\ 0 & 4 & 7 \\end{bmatrix}\\), then find 3A – 2B.<\/p>\n We have, 3A – 2B = 3A + (-2)B<\/p>\n \\(\\implies\\) 3A – 2B = \\(\\begin{bmatrix} 6 & 9 & 12 \\\\ 0 & 12 & 18 \\\\ 15 & 24 & 27 \\end{bmatrix}\\) -\\(\\begin{bmatrix} -6 & 0 & -10 \\\\ -10 & -6 & -4 \\\\ 0 & -8 & -14 \\end{bmatrix}\\)<\/p>\n = \\(\\begin{bmatrix} 0 & 9 & 2 \\\\ -10 & 6 & 14 \\\\ 15 & 16 & 13 \\end{bmatrix}\\)<\/p>\n\n\n Example : <\/span>If A = \\(\\begin{bmatrix} 2 & 3 & -5 \\\\ 1 & 2 & -1 \\end{bmatrix}\\) and B = \\(\\begin{bmatrix} 0 & 5 & 1 \\\\ -2 & 7 & 3 \\end{bmatrix}\\), then find A + B and A – B.<\/p>\n Solution : <\/span>Clearly A and B both are matrices of the same order \\(2\\times 3\\). So, A + B and A – B both are defined.Subtraction of matrices of order \\(2\\times 2\\)<\/strong><\/h4>\n
Subtraction of matrices of order \\(3\\times 3\\)<\/strong><\/h4>\n
\nNow, A + B = \\(\\begin{bmatrix} 2 & 3 & -5 \\\\ 1 & 2 & -1 \\end{bmatrix}\\) + \\(\\begin{bmatrix} 0 & 5 & 1 \\\\ -2 & 7 & 3 \\end{bmatrix}\\)
\n= \\(\\begin{bmatrix} 2 & 8 & -4 \\\\ -1 & 9 & 2 \\end{bmatrix}\\)
\nand A – B = A + (-B) = \\(\\begin{bmatrix} 2 & 3 & -5 \\\\ 1 & 2 & -1 \\end{bmatrix}\\) + (-1)\\(\\begin{bmatrix} 0 & 5 & 1 \\\\ -2 & 7 & 3 \\end{bmatrix}\\)
\n= \\(\\begin{bmatrix} 2 & -2 & -6 \\\\ 3 & -5 & -4 \\end{bmatrix}\\)
<\/p>\n\n\n\n