Solved: Suppose that the characteristic polynomial of some matrix A is found to be p() =
Chapter 5, Problem 27(choose chapter or problem)
Suppose that the characteristic polynomial of some matrix A is found to be p() = ( 1)( 3)2( 4)3. In each part, answer the question and explain your reasoning. (a) What can you say about the dimensions of the eigenspaces of A? (b) What can you say about the dimensions of the eigenspaces if you know that A is diagonalizable? (c) If {v1, v2, v3} is a linearly independent set of eigenvectors of A, all of which correspond to the same eigenvalue of A, what can you say about that eigenvalue?
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