Suppose that A is a 4 x 4 matrix in the block form. A= [~
Chapter , Problem 53(choose chapter or problem)
Suppose that A is a 4 x 4 matrix in the block form. A= [~ g]. where the blocks are all 2 x 2 matrices. (a) Use a random matrix for A to illustrate that A 2 = [~2 ; 2]. where * represents some 2 x 2 matrix. (b) Use a random matrix for A to illustrate that A3 = [ ~ ; 3]. where * represents some 2 x 2 matrix. (c) Make a conjecture about the block form of Ak, where k is a positive integer. (d) Prove your conjecture for k = 3.
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