Question

In Problems 13–16, use the following matrices to compute each expression.

$A=\left[\begin{array}{cc}1& 0\\ 2& 4\\ -1& 2\end{array}\right]B=\left[\begin{array}{ccc}4& -3& 0\\ 1& 1& -2\end{array}\right]C=\left[\begin{array}{cc}3& -4\\ 1& 5\\ 5& 2\end{array}\right]$

$BC$

Short answer

$BC=\left[\begin{array}{cc}9& -31\\ -6& -3\end{array}\right]$

Step-by-step solution

Step 1. Given information

The given matrices are

$A=\left[\begin{array}{cc}1& 0\\ 2& 4\\ -1& 2\end{array}\right]B=\left[\begin{array}{ccc}4& -3& 0\\ 1& 1& -2\end{array}\right]C=\left[\begin{array}{cc}3& -4\\ 1& 5\\ 5& 2\end{array}\right]$

Step 2. Find the value of expression BC.

$$\begin{gathered} BC \\ =\left[\begin{array}{ccc}4& -3& 0\\ 1& 1& -2\end{array}\right]\left[\begin{array}{cc}3& -4\\ 1& 5\\ 5& 2\end{array}\right] \\ =\left[\begin{array}{cc}4·3+\left(-3\right)·1+0·5& 4·\left(-4\right)+\left(-3\right)·5+0·2\\ 1·3+1·1+\left(-2\right)·5& 1·\left(-4\right)+1·5+\left(-2\right)·2\end{array}\right] \\ =\left[\begin{array}{cc}9& -31\\ -6& -3\end{array}\right] \end{gathered}$$