Find the characteristic equation and eigenvalues of the matrix and a basis for each of the corresponding eigenspaces. 12 -4 A = -3 1 the characteristic equation the eigenvalues (Enter your answers from smallest to largest.) a basis for each of the corresponding eigenspaces B, = B, = For the matrix A, use the basis of the eigenspaces to find a nonsingular matrix P such that P-1AP is diagonal. P = Verify that P-AP is a diagonal matrix with the eigenvalues on the main diagonal. P-'AP

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