(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have a matrix A [1 -1 -1 -1; -1 1 -1 -1; -1 -1 1 -1; -1 -1 -1 1], its characteristic polynomial p(t) = (t + 2)(t-2)^{3}, and given value of lambda = 2. I need to find basis for eigenspace, and determine algebraic and geometric multiplicities of labmda.

2. Relevant equations

3. The attempt at a solution

I did find the basis, and geometric multiplicity (the dimention of eigenspace).. but I cant figure out how to figure out algebraic multiplicity! I know the correct answer is 3, but why? i was trying to find simple explanation of alg. mult. on google, but the answer come up waay too tangled up for me to understand :-S

EDIT: Is it because the characteristic polynomial is p(t) = (t + 2)(t-2)^{3}and since my lambda = 2, i need to take (t-2)^{3}(which is t-2=0 => t=2), and the power is the value of algebraic mult...? am I on the right track?

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# Algebraic multiplicity

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