Question

If $A = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix}$, then find the value of $(A + B)$ and $(A - B)$.

Hint:

Matrix addition and subtraction are performed by adding or subtracting corresponding elements of the two matrices.

Answer 1

We are given two matrices: \[ A = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix}, B = \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix} \]

Step 1: Find $(A + B)$. \[ A + B = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix} + \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix} = \begin{bmatrix} (2+1) & (4+3) \\ (3+(-2)) & (2+5) \end{bmatrix} = \begin{bmatrix} 3 & 7 \\ 1 & 7 \end{bmatrix} \] Step 2: Find $(A - B)$. \[ A - B = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix} - \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix} = \begin{bmatrix} (2-1) & (4-3) \\ (3-(-2)) & (2-5) \end{bmatrix} = \begin{bmatrix} 1 & 1 \\ 5 & -3 \end{bmatrix} \]

Final Answer: \[ A + B = \begin{bmatrix} 3 & 7 \\ 1 & 7 \end{bmatrix}, A - B = \begin{bmatrix} 1 & 1 \\ 5 & -3 \end{bmatrix} \]