Chapter 9, Problem 3P

Three matrices are defined as

$\left[A\right]=\left[\begin{array}{c}1\\ 3\\ 7\end{array}\begin{array}{c}6\\ 10\\ 4\end{array}\right]\left[B\right]=\left[\begin{array}{cc}1& 3\\ 0.5& 2\end{array}\right]\left[C\right]=\left[\begin{array}{cc}2& -2\\ -3& 1\end{array}\right]$

(a) Perform all possible multiplications that can be computed between pairs of these matrices.

(b) Use the method in Box PT3.2 to justify why the remaining pairs cannot be multiplied.

(c) Use the results of (a) to illustrate why the order of multiplication is important.