(a) Find the eigenvalues and corresponding eigenvectors of the following matrix: 0-4 A = 0 5 4 -4 4 3 ·( X₁ = [1, -2]T, and A₂ = -3 with eigenvector X₂ = [1,-1]. 1 If P is a matrix such that P = ( X₁ X₂ ) = (-¹/2-¹₁), s show that P-¹AP -1 gives a diagonal matrix with the same eigenvalues as A. (b) The matrix A = -5-2 has eigenvalues X₁ = -1 with eigenvector 1

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