Oh it gives me headache... been thinking on this problem for a while, and don't even know where to begin! Could any one give me a hint at least?? :((adsbygoogle = window.adsbygoogle || []).push({});

Problem:

Let A be (3x3) matrix : [ 4 -2 2; 2 4 -4; 1 1 0] andu(vector) = [1 3 2].

a) Verify that Au= 2u

I got this one without a problem.

b) Without forming A^5, calculate the vector A^5*u.

This is where I get stuck.. I've tried to search, but keep coming up with some equations that involve eigenvalues (which I havent studied yet..). So, im assuming that i don't have to use any of eigenvalues.. Is there any other way?

I tried to replace A matrix with [a b c; d...] values, and take first 3 powers of that, but its way too hard to keep track of everything..

So, any hint?? :(

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# Matrix^n without eigenvalues

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