1. The problem statement, all variables and given/known data Determine if this matrix is diagonalizable and explain why or why not. [ 2 1 0 0 0 ] [ 0 2 1 0 0 ] [ 0 0 2 1 0 ] [ 0 0 0 2 1 ] [ 0 0 0 0 2 ] 2. Relevant equations No equations provided and the use of a calculator will be prohibited on the test, so thats out of the question. I can find the determinant via expansion, but that doesn't help really. 3. The attempt at a solution So I'm pretty confident that this is not diagonalizable because the only eigenvalue seems to be 2 with multiplicity 5, although i'm not sure that actually proves anything. Additionally, I'm fairly certain that because the study guide has this as a 5x5 matrix with calculator use prohibited, there must be a way, just from the shape, to determine whether it's diagonalizable. Does anyone have any tips? Thank you so much for any help!