Chapter 3, Problem 29P

Create the following three matrices:

$A=\left[\begin{array}{ccc}1& -3& 5\\ 2& 2& 4\\ -2& 0& 6\end{array}\right]B=\left[\begin{array}{ccc}0& -2& 1\\ 5& 1& -6\\ 2& 7& -1\end{array}\right]C=\left[\begin{array}{ccc}-3& 4& -1\\ 0& 8& 2\\ -3& 5& 3\end{array}\right]$

(a) Calculate A+B and B +A to show that addition of matrices is commutative.

(b) Calculate A + (B + C) and (A + B) + C to show that addition of matrices is associative.

(c) Calculate 3 (A + C) and 3A + 5C to show that, when matrices are multiplied by a scalar, the multiplication is distributive.

(d) Calculate A*(B + C) and A*B + A*C to show that matrix multiplication is distributive.