Question

Find f(A) = A^100 for A=[1 2 0 2] matrix by using Carley-Hamlton theory principles

Answer 1

A×4 = E, so A = E/4
B/4 = E, so B = 4E
C+4 = E, so C = E=4
D-4 = E, so D = E+4
and
A+B+C+D=100.

now substitute the values that we got of A, B, C and D in the equation, to get,
(E/4) + 4E + E-4 + E+4 = 100
(E/4) + 4E + 2E = 100
(E/4) + 6E = 100
(E+24E)/4 = 100
E+24E = 100×4
25E = 400
E = 400/25
E = 16

i answered same question before too ....

Hope it helps !!!