USA: +1 (725) 712-1730 
Sign in
Let A = [-8 15 15 -8 13 10 3 -5 -4]. (a) Use MATLAB to compute A^n for n = 2, 3, 4, 5, 6, 7, 8. Do you notice a pattern? (b) Have MATLAB produce an invertible P and a diagonal D such that A = PDP^-1, Notice that complex numbers get involved. (c) To understand A^n, it suffices to understand D^n because A^n = PD^n P^-1. Describe the pattern that emerges when we consider powers of D: D, D^2, D^3, D^4, etc. (d) Without doing a computation in MATLAB, determine A^1000001
Expert Answer
a)
An*4=I (Identity matrix) where n=1,2,3. and so on
so An*4+1 =A where n=1,2,3….and so on
b)
c)
we can observe that D4 = I (Identity matrix)
and the pattern is D4*n = I where n=1,2,3 … and so on
D4*n+1 = D where n=1,2,3 … and so on
d) To determine A10000001 by 4 divisibility rule we know that 10000001 gives remainder 1
so it is in the pattern A4*n+1 which is equal to A
so A10000001 = A
