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Homework Statement
Given the matrix
0 1 0
0 0 1
-3 -7 -5
Find the eigenspaces for the various eigenvalues
Prove that there cannot be a basis of R3 consisting entirely of eigenvectors of A
Homework Equations
The Attempt at a Solution
The eigenvectors are not a problem, I end up with (λ+3)(λ+1)2 so my eigenvalues are -3 and -1. Substituting in I get [1, -3, 9] and [1, -1, 1]. Now would the eigenspace simply be {[1, -3, 9], [1, -1, 1], [0, 0, 0]} or am I missing some other step?
Also, how can I prove there cannot be a basis of R3 consisting of eigenvectors of A? Could it just be because there must be n vectors in a basis of Rn?
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