Chapter 3 Linear Systems and Matrices - 3.8 Use Inverse Matrices to Solve Linear Systems - 3.8 Exercises - Quiz for Lessons 3.6-3.8 - Page 217: 3

$A(B+C)=\begin{bmatrix} -12 & -24\\ -16 & -10 \end{bmatrix}$

$A(B+C)=\begin{bmatrix} 1 & -4\\ 5 & 2 \end{bmatrix}.(\begin{bmatrix} 2 &-3\\ 0 & 1 \end{bmatrix}+\begin{bmatrix} -6 &-1\\ 2 & 4 \end{bmatrix})$ $=\begin{bmatrix} 1 & -4\\ 5 & 2 \end{bmatrix}(\begin{bmatrix} 2+(-6) & -3+(-1)\\ 0+2 & 1+4 \end{bmatrix})$ $=\begin{bmatrix} 1 & -4\\ 5 & 2 \end{bmatrix}.\begin{bmatrix} -4 & -4\\ 2 & 5 \end{bmatrix}$ $=\begin{bmatrix} 1 & -4\\ 5 & 2 \end{bmatrix}$ $=\begin{bmatrix} -12 & -24\\ -16 & -10 \end{bmatrix}$