Question

use the given matrices to compute each

expression.

$$\begin{gathered} A=\left[\begin{array}{cc}1& -1\\ 0& -4\\ 3& -2\end{array}\right] \\ B=\left[\begin{array}{ccc}1& -2& 5\\ 0& 3& 1\end{array}\right] \\ C=\left[\begin{array}{cc}4& 6\\ 1& -3\\ -1& 8\end{array}\right] \end{gathered}$$

$BA$

Short answer

The evaluation of the expression would be

$BA=\left[\begin{array}{cc}16& 17\\ 3& -10\end{array}\right]$

Step-by-step solution

Step 1. Given

$$\begin{gathered} A=\left[\begin{array}{cc}1& -1\\ 0& -4\\ 3& -2\end{array}\right] \\ B=\left[\begin{array}{ccc}1& -2& 5\\ 0& 3& 1\end{array}\right] \\ C=\left[\begin{array}{cc}4& 6\\ 1& -3\\ -1& 8\end{array}\right] \end{gathered}$$

Step 2. Calculation

$$\begin{gathered} BA=\left[\begin{array}{ccc}1& -2& 5\\ 0& 3& 1\end{array}\right]\left[\begin{array}{cc}1& -1\\ 0& -4\\ 3& -2\end{array}\right] \\ =\left[\begin{array}{cc}1\left(1\right)+0(-2)+5\left(3\right)& 1(-1)+(-2)(-4)+5(-2)\\ 0\left(1\right)+3\left(0\right)+1\left(3\right)& 0(-1)+3(-4)+1(-2)\end{array}\right] \\ =\left[\begin{array}{cc}16& 17\\ 3& -10\end{array}\right] \end{gathered}$$