Hi all, I have a hw problem that I would like someone to check:(adsbygoogle = window.adsbygoogle || []).push({});

this relates to the eigenvectors: in the problem we are given characteristic polynomial, where I put x instead of lambda:

p(x) = x^2*(x+5)^3*(x -7)^5

Also given A is a square matrix, and then these questions (my answers):

- size of A? (10x10?? by looking at the multiplicities?)

- can A be invertible? (I think "no", otherwise there's no eigenvectors would be possible to find)

- possible dimensions for nullspace of A (at least 3 and at most 10?)

- what can be said about dim. of x = 7 eigenspace? (that according to its multiplicity, dim. can be at most 5 but at least 1?)

Do I understand correctly this whole "multiplicity" concept? I am really shaky on the first question.

Thanks in advance.

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# Multiplicity and dimension

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