Name:			Date:
Multiplying Matrices.

1) $\left[\begin{array}{cc}-7& 2\\ -8& 3\end{array}\right].\left[\begin{array}{cc}4& -6\\ 5& -7\end{array}\right]$	2) $\left[\begin{array}{cc}-4& 3\\ -2& 1\end{array}\right].\left[\begin{array}{cc}6& -2\\ 2& -3\end{array}\right]$
3) $\left[\begin{array}{ccc}2& 3& 4\\ 4& 6& 8\end{array}\right].\left[\begin{array}{ccc}2& 3& -4\\ 3& -6& 2\end{array}\right]$	4) $\left[\begin{array}{c}-2\\ 3\\ 1\end{array}\right].\left[\begin{array}{cc}1& -2\end{array}\right]$
5) $\left[\begin{array}{cc}-10& \mathrm{-q}\\ -4p& -3\end{array}\right].\left[\begin{array}{cc}-3p& 0\\ 2q& -10\end{array}\right]$	6) $\left[\begin{array}{cc}4& -6\\ -3& 4\\ -3& -5\end{array}\right].\left[\begin{array}{cc}-1& 2\\ 2& 2\end{array}\right]$
7) $\left[\begin{array}{cc}10& 2\\ -6& 4\\ -8& 2\end{array}\right].\left[\begin{array}{cc}-3& 2\\ -1& -3\end{array}\right]$	8) $\left[\begin{array}{c}-2\\ 3\\ 0\end{array}\right].\left[\begin{array}{cc}2& -1\end{array}\right]$
9) $\left[\begin{array}{ccc}-6& 3& -7\\ 2& 3& -1\\ 4& -1& 2\\ 0& 1& 3\end{array}\right].\left[\begin{array}{cc}2& 4\\ 3& -2\\ 1& 0\end{array}\right]$	10) $\left[\begin{array}{c}-4\\ 3\\ 2\end{array}\right].\left[\begin{array}{cc}6& -4\end{array}\right]$
11) $\left[\begin{array}{cc}-6& -2\\ -2& 1\\ 4& 2\\ 0& -3\end{array}\right].\left[\begin{array}{ccc}0& -1& 2\\ -3& 1& -5\end{array}\right]$	12) $\left[\begin{array}{cc}-2& 1\\ -3& 4\end{array}\right].\left[\begin{array}{cc}2& -3\\ 1& -4\end{array}\right]$
13) $\left[\begin{array}{cc}7& 2\\ -3& -4\end{array}\right].\left[\begin{array}{cc}6& -2\\ 3& 4\end{array}\right]$	14) $\left[\begin{array}{cc}-10& -4\\ -6& 3\end{array}\right].\left[\begin{array}{cc}-2& -1\\ 4& 2\end{array}\right]$
15) $\left[\begin{array}{c}6\\ -7\end{array}\right].\left[\begin{array}{cc}-3& 4\end{array}\right]$	16) $\left[\begin{array}{cc}10& -5n\end{array}\right].\left[\begin{array}{cc}-10m& -2n\\ 3& 4\end{array}\right]$
17) $\left[\begin{array}{ccc}3& 4& 6\\ 3& 2& 1\end{array}\right].\left[\begin{array}{ccc}4& 2& -4\\ 3& -6& 2\end{array}\right]$	18) $\left[\begin{array}{ccc}4& 0& 8\\ 3& 1& 2\end{array}\right].\left[\begin{array}{cc}-2& 2\\ -4& 3\\ 1& -2\end{array}\right]$
19) $\left[\begin{array}{cc}7& 8\\ 4& -10\end{array}\right].\left[\begin{array}{c}-3\\ 1\end{array}\right]$	20) $\left[\begin{array}{cc}5& -6q\end{array}\right].\left[\begin{array}{cc}-3p& -4q\\ 3& 5\end{array}\right]$

 

Answers:

1) $\left[\begin{array}{cc}-18& 28\\ -17& 27\end{array}\right]$	2) $\left[\begin{array}{cc}-18& -1\\ -10& 1\end{array}\right]$
3) undefined	4) $\left[\begin{array}{cc}-2& 4\\ 3& -6\\ 1& -2\end{array}\right]$
5) $\left[\begin{array}{cc}30p-2q^2& 10q\\ 12p^2-6q& 30\end{array}\right]$	6) $\left[\begin{array}{cc}-16& -4\\ 11& 2\\ -7& -16\end{array}\right]$
7) $\left[\begin{array}{cc}-32& 14\\ 14& -24\\ 22& -22\end{array}\right]$	8) $\left[\begin{array}{cc}-4& 2\\ 6& -3\\ 0& 0\end{array}\right]$
9) $\left[\begin{array}{cc}-10& -30\\ 12& 2\\ 7& 18\\ 6& -2\end{array}\right]$	10) $\left[\begin{array}{cc}-24& 16\\ 18& -12\\ 12& -8\end{array}\right]$
11) $\left[\begin{array}{ccc}6& 4& -2\\ -3& 3& -9\\ -6& -2& -2\\ 9& -3& 15\end{array}\right]$	12) $\left[\begin{array}{cc}-3& 2\\ -2& -7\end{array}\right]$
13) $\left[\begin{array}{cc}48& -6\\ -30& -10\end{array}\right]$	14) $\left[\begin{array}{cc}4& 2\\ 24& 12\end{array}\right]$
15) $\left[\begin{array}{cc}-18& 24\\ 21& -28\end{array}\right]$	16) $\left[\begin{array}{cc}-100m-15n& -40n\end{array}\right]$
17) undefined	18) $\left[\begin{array}{cc}0& -8\\ -8& 5\end{array}\right]$
19) $\left[\begin{array}{c}-13\\ -22\end{array}\right]$	20) $\left[\begin{array}{cc}-15p-18q& -50q\end{array}\right]$