Question: Q3 (8 points) Let B be a 5 x 5 matrix with eigenvalues: 1 = 12 = 1 with corresponding eigenvectors s + 2t, 5

Q3 (8 points) Let B be a 5 x 5 matrix with eigenvalues: 1 = 12 = 1 with corresponding eigenvectors s + 2t, 5 - t, s, 9t, -s , s, tER, not both 0. 13 = -3 with corresponding eigenvectors 3r, 0, -5r, 7r, 4r , rER,r / 0. 14 = 15 = 0 with corresponding eigenvectors 4p 2q 3q, 3p, 5 3 ' 2 , 9 , P,qER, not both 0 Answer the following questions: (a) [2 points] Is the matrix B an invertible matrix? Justify. (b) [2 points] Is the matrix B a diagonalizable matrix? Justify. (c) [4 points] Find an invertible matrix P and a diagonal matrix D that satisfy P-1BP = D

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