## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$\begin{bmatrix} 50 & -3\\ 18 & 21 \end{bmatrix}$
Since, $A+B$ is a $2 \times 3$ matrix and $C$ is a $3 \times 2$ matrix, we know that $(A+B)C$ is defined and results in a $2 \times 2$ matrix. $A+B=\begin{bmatrix} 0+4 & 3+1 & -5+0\\ 1+(-2) & 2+3 & 6+(-2) \end{bmatrix}\\=\begin{bmatrix} 4 & 4 & -5 \\ 1-2 & 5 & 6-2 \end{bmatrix}\\=\begin{bmatrix} 4 & 4 & -5\\ -1 & 5 & 4 \end{bmatrix}$ Now, $(A+B)C=\left[\begin{array}{lll} 4 & 4 & -5\\ -1 & 5 & 4 \end{array}\right]\left[\begin{array}{ll} 4 & 1\\ 6 & 2\\ -2 & 3 \end{array}\right] \\=\left[\begin{array}{ll} 16+24+10 & 4+8-15\\ -4+30-8 & -1+10+12 \end{array}\right] \\=\begin{bmatrix} 50 & -3\\ 18 & 21 \end{bmatrix}$