Addition and Subtraction of a Matrix

Addition of a Matrix

If A and B are two matrices of the same order, then their sum A+B is defined and is

obtained by adding the corresponding elements of A and B .

In other words, if $A = [a_{ij}]_{m\times n} \ and \ B = [b_{ij}]_{m\times n}$ are matrices of same order, then A+B
is defined and is given by

$A + B = [c_{ij}]_{m\times n} \ , \ where \ [c_{ij}]=[a_{ij}]+[b_{ij}]$

For example : if $A = \begin{bmatrix} 2 & 3 &6 \\ 4& 0& 9 \end{bmatrix} \ and \ B = \begin{bmatrix} 0 & 6 &8 \\ 7& 0& 8 \end{bmatrix}$

$then \ A+B= \begin{bmatrix} 2+0 &3+6 &6+8 \\ 4+7&0+0 &9+8 \end{bmatrix} = \begin{bmatrix} 2 &9 & 14\\ 11&0 &17 \end{bmatrix}$
Remark : If two matrices are not of the same order, their sum is not defined.

Subtraction or Difference of a Matrix

If A and B are two matrices of the same order, then their difference A-B is defined and is

obtained by subtracting the elements of B from the corresponding elements of A .

For example : if

$A=\begin{bmatrix} 4 & 3\\ 6 & 8\\ 9 &15 \end{bmatrix} \ ,\ B=\begin{bmatrix} 3 & 8\\ 11 & 7\\ 6 &8 \end{bmatrix} \ ,\\$

$then\ A-B=\begin{bmatrix} 4-3 & 3-8\\ 6-11 & 8-7\\ 9-6 &15-8 \end{bmatrix} = \begin{bmatrix} 1 & -5\\ -5 & 1\\ 3 &7 \end{bmatrix} \ .$
Remark : By definition A - B is same as the matrix A + ( - B ) .

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Addition and Subtraction of a Matrix

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