Let the matrix A = {8, - 5,6, - 3} and the vector α = {6,7} be the quintic power α of a and the 100th power α of A | Math enthusiast | Mathematical art

Let the matrix A = {8, - 5,6, - 3} and the vector α = {6,7} be the quintic power α of a and the 100th power α of A

method:
|A-λE|=(2-λ)(3-λ)
The basic solution system of (a-3e) x = 0 is B1 = (1,1) ^ t
The basic solution system of (a-2e) x = 0 is B2 = (5,6) ^ t
α=b1+b2
A^5α = 3^5b1+2^5b2
A^100α = 3^100b1+2^100b2

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