Question: Given is a 3 X 3 matrix A so that 0 0 1 3 0 0 0 0 1 A = 3 2 9 0

Given is a 3 X 3 matrix A so that 0 0 1 3 0 0 0 0 1 A = 3 2 9 0 5 0 3 2 9 1 0 3 0 0 3 1 0 3 Do not compute this matrix product - it would only make your life harder H! a) Find three linearly independent eigenvectors of A, and the corresponding eigenvalues. b) Show linear independence of the vectors you found. You can use any Theorems from WorkScripts 0-10 here, after stating them. c) Explain why your answers to a) are eigenvectors and eigenvalues, using only denitions and algebraic manipulations (without appealing to Theorems)

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