Question

I need help on this practice question on my prep guide

Answer 1

We are given the following two matrices

`A=\begin{bmatrix}-1 & 6 \\ -2 & 2 \\ 4 & 9 \\ -5 & -11\end{bmatrix}\; and\; B=\begin{bmatrix}7 & -11 \\ -3 & -1 \\ 9 & -3 \\ -10 & 2\end{bmatrix}`

We are asked to find B + A

Recall that matrix addition is commutative meaning that A+B is the same as B+A

The size of both matrices A and B is the same (4x2) hence matrix addition is possible.

Simply add the corresponding entries of the matrices.

`\begin{bmatrix}-1 & 6 \\ -2 & 2 \\ 4 & 9 \\ -5 & -11\end{bmatrix}\; +\begin{bmatrix}7 & -11 \\ -3 & -1 \\ 9 & -3 \\ -10 & 2\end{bmatrix}=\begin{bmatrix}-1+7 & 6+(-11)_{} \\ -2+(-3) & 2+(-1)_{} \\ 4+9 & 9+(-3) \\ -5+(-10) & -11+2\end{bmatrix}=\begin{bmatrix}-1+7 & 6-11_{} \\ -2-3 & 2-1_{} \\ 4+9 & 9-3 \\ -5-10 & -11+2\end{bmatrix}=\begin{bmatrix}6 & -5_{} \\ -5 & 1_{} \\ 13 & 6 \\ -15 & -9\end{bmatrix}`

Therefore, the result of the matrix addition B+A is

`B+A=\begin{bmatrix}6 & -5_{} \\ -5 & 1_{} \\ 13 & 6 \\ -15 & -9\end{bmatrix}`