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Given matrices A and B, find A+B and A-B.

May 23, 2026Mathematics

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2 parts

\begin{bmatrix} 5 & 5 & 12 \\ 9 & 9 & 13 \end{bmatrix}

\begin{bmatrix} 3 & 5 & 0 \\ 5 & 7 & 5 \end{bmatrix}

4 steps

Given the matrices:

A = \begin{bmatrix} 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}

B = \begin{bmatrix} 1 & 0 & 6 \\ 2 & 1 & 4 \end{bmatrix}

Find $A+B$

Add the corresponding elements of matrix A and matrix B.
$A+B = \begin{bmatrix} 4+1 & 5+0 & 6+6 \\ 7+2 & 8+1 & 9+4 \end{bmatrix}$
Perform the addition for each element.
$A+B = \begin{bmatrix} 5 & 5 & 12 \\ 9 & 9 & 13 \end{bmatrix}$
The sum of the matrices is:
$\boxed{\begin{bmatrix} 5 & 5 & 12 \\ 9 & 9 & 13 \end{bmatrix}}$

Find $A-B$

Subtract the corresponding elements of matrix B from matrix A.
$A-B = \begin{bmatrix} 4-1 & 5-0 & 6-6 \\ 7-2 & 8-1 & 9-4 \end{bmatrix}$
Perform the subtraction for each element.
$A-B = \begin{bmatrix} 3 & 5 & 0 \\ 5 & 7 & 5 \end{bmatrix}$
The difference of the matrices is:
$\boxed{\begin{bmatrix} 3 & 5 & 0 \\ 5 & 7 & 5 \end{bmatrix}}$

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