Chapter 3, Problem 29P

Create the following three matrices:

A= $\begin{array}{ccc}5& -3& 7\\ 2& 0& -6\\ -4& 8& 9\end{array}$ B $\begin{array}{ccc}3& 2& -1\\ 6& 8& -7\\ 4& 4& 0\end{array}$ = C $\begin{array}{ccc}-9& 8& 3\\ 1& 7& -5\\ 3& 3& 6\end{array}$ =

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 multiplication of matrices is associative.

(c) Calculate 5(B+C) and 5B+5C to show that, when matrices are multip lied by a scalar, the multiplication is distributive.

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