Problem
18. Multiply: \[ \left[\begin{array}{cc} 2 & -1 \\ 3 & 4 \end{array}\right] \bullet\left[\begin{array}{ccc} 3 & -9 & -2 \\ 5 & 7 & -6 \end{array}\right] \] $\left[\begin{array}{ccc}1 & -25 & 2 \\ 29 & 1 & -30\end{array}\right]$ $\left[\begin{array}{ccc}6 & -10 & 13 \\ 9 & 8 & -5\end{array}\right]$ $\left[\begin{array}{ccc}5 & -12 & 8 \\ 10 & 8 & 16\end{array}\right]$ $\left[\begin{array}{ccc}12 & 17 & 4 \\ 14 & -20 & 18\end{array}\right]$
Solution
Step 1 ：We have that
Step 2 ：\[\begin{pmatrix} 2 & -1 \\ 3 & 4 \end{pmatrix} \begin{pmatrix} 3 & -9 & -2 \\ 5 & 7 & -6 \end{pmatrix} = \begin{pmatrix} (2)(3) + (-1)(5) & (2)(-9) + (-1)(7) & (2)(-2) + (-1)(-6) \\ (3)(3) + (4)(5) & (3)(-9) + (4)(7) & (3)(-2) + (4)(-6) \end{pmatrix}\]
Step 3 ：= \[\begin{pmatrix} 1 & -25 & 2 \\ 29 & 1 & -30 \end{pmatrix}\]
Step 4 ：\[\boxed{\begin{pmatrix} 1 & -25 & 2 \\ 29 & 1 & -30 \end{pmatrix}}\]
