4 1 3 0 6. Let A = -1 2 0 4 1 2 (a) calculate determinants.) Find the characteristic polynomial of A. (Feel free to use WolframAlpha to (b) WolframAlpha to help factor the characteristic polynomial.) Find all eigenvalues of A and their algebraic multiplicities. (You may use (c) For each eigenvalue of A, find a basis for the corresponding eigenspace. (d) If possible, diagonalize A; if this is not possible, then explain why not.

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