Hi all, I have a hw problem that I would like someone to check: 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.