In Exercise 53, use either a calculator with matrix capabilities or computer software su...

In Exercise 53, use either a calculator with matrix capabilities or computer software such as MATLAB to solve each problem.

Suppose that A is a 4 x 4 matrix in the block form,

where the blocks are all 2 x 2 matrices.

(a) Use a random matrix for A to illustrate that where * represents some 2 x 2 matrix.

(b) Use a random matrix for A to illustrate that where * represents some 2 x 2 matrix.

(c) Make a conjecture about the block form of , where k is a positive integer.

(d) Prove your conjecture for k = 3.