Question

$\

$$\begin{bmatrix} 17 \\\\ -49 \\\\ -5 \\end{bmatrix}$$

+\

$$\begin{bmatrix} 12 \\\\ 23 \\\\ -3 \\end{bmatrix}$$

=$
$\

$$\begin{bmatrix} 43 & 17 \\\\ -27 & 28 \\\\ 18 & 37 \\end{bmatrix}$$

+\

$$\begin{bmatrix} 2 & 18 \\\\ 16 & 3 \\\\ -11 & -6 \\end{bmatrix}$$

=$

Explanation:

Step1: Add first vector elements

$$\begin{bmatrix} 17+12 \\ -49+23 \\ -5+(-3) \end{bmatrix}$$

Step2: Calculate vector sums

$$\begin{bmatrix} 29 \\ -26 \\ -8 \end{bmatrix}$$

Step3: Add matrix elements entry-wise

$$\begin{bmatrix} 43+2 & 17+18 \\ -27+16 & 28+3 \\ 18+(-11) & 37+(-6) \end{bmatrix}$$

Step4: Compute matrix sums

$$\begin{bmatrix} 45 & 35 \\ -11 & 31 \\ 7 & 31 \end{bmatrix}$$

Answer:

$$\begin{bmatrix} 29 \\ -26 \\ -8 \end{bmatrix}$$

$$\begin{bmatrix} 45 & 35 \\ -11 & 31 \\ 7 & 31 \end{bmatrix}$$