Find p, q for which$\left( \begin{matrix} 2p & 8 \\ 3 & -5q \\\end{matrix} \right)\left( \begin{align} & 1 \\ & 2 \\\end{align} \right)=\left( \begin{align} & 24 \\ & -17 \\\end{align} \right)$
–4, 2
4, 2
–4, –2
4, –2
$\begin{align} & \left( \begin{matrix} 2p & 8 \\ 3 & -5q \\\end{matrix} \right)\left( \begin{align} & 1 \\ & 2 \\\end{align} \right)=\left( \begin{align} & 24 \\ & -17 \\\end{align} \right) \\ & \left[ \begin{align} & (2p\times 1)+(8\times 2) \\ & (3\times 1)+(-5q\times 2) \\\end{align} \right]=\left( \begin{align} & 24 \\ & -17 \\\end{align} \right) \\ & \left( \begin{align} & 2p+16 \\ & 3-10q \\\end{align} \right)=\left( \begin{align} & 24 \\ & -17 \\\end{align} \right) \\ & \text{Using equality of matrices} \\ & 2p+16=24 \\ & 2p=8,\text{ }p=4 \\ & \text{also} \\ & 3-10q=-17 \\ & 10q=20 \\ & q=2 \\ & (p,q)=(4,2) \\\end{align}$