1.

It is often useful to partition matrices into a collection of submatrices. For example, the matrices 12- 2 -1 7 0 A3-3and B3 045 -2-3 1 can be partitioned into 217 A11 : A12 AziA2z BBi2 B21B 3 0 45 -2-31 a. Show that the product of A and B in this case is AB b. If B were instead partitioned into 217 B1B -2 1-3 would the result in part (a) hold? Make a conjecture concerning the conditions necessary for the result in part (a) to hold in the general case. c