-1 -3 3 A = 3 6 -7 3 -62 Let A be (a) Find the characteristic polynomial and the eigenvalues of A. State the algebraic multiplicity of each eigenvalue of A. (Hint: To compute det(A-AI) consider initial steps of applying C1+C2 and then R2-R1.) (b) Find a basis for each eigenspace of A. State the geometric multiplicity of each eigenvalue of A. (c) A is diagonalizable. Explain why. Diagonalize A, that is, find an invertible matrix P and a diagonal matrix D such that P-1AP=D.

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