Chapter 5 - Section 5.7 - Properties of Matrices - 5.7 Exercises - Page 553: 9

$a=\frac{3}{4}\\ p=3 \\ r=3 \\ z=18$

Two matrices are equal when the two matrices are of the same size and when their corresponding elements are equal to each other. Firstly, we will find the sum of two matrices of the same size on the left side of the given equality: $\begin{bmatrix} -7+z&4r &8s \\6p &2&5\end{bmatrix} + \begin{bmatrix} -9&8r &3 \\2&5&4\end{bmatrix} =\begin{bmatrix} -7+z-9 &4r+8r &8s+3 \\6p+2&7&9\end{bmatrix} $ So the given equation simplifies to: $\begin{bmatrix} -16+z & 12r &8s+3 \\6p+2&7&9\end{bmatrix} =\begin{bmatrix}2 &36 &27 \\20&7&12a\end{bmatrix} $ Equate each pair of corresponding elements that involve a variable to obtain: \begin{align*} -16+z&=2 \\ z&=2+16\\ z&=18\\ \\\\ 12r&=36\\ r&=\frac{36}{12}\\ r&=3\\ \\\\ 6p+2&=20\\ 6p&=20-2\\ 6p&=18\\ p&=\frac{18}{6}\\p&=3\\ \\\\ 12a&=9\\ a&=\frac{9}{12}\\ a&=\frac{3}{4} \end{align*}