1) Which of the following statements are correct? a) A square matrix A is not invertible if and only if A = 0 is an eigenvalue of A. b) If v and v2 are linearly independent eigenvectors of a matrix A, then they correspond to different eigenvalues. c) If a square matrix A is triangular, then the eigenvalues of A are the entries on its main diagonal. 5 d) A = 5 is an eigenvalue ofA = e) Let A be an n x n matrix. If det(A AIn) f) Suppose A is a 3 x 3 matrix having eigenvalues -1, 1, 2. Ak is diagonalizable for any integer k > 0. = 0 for some dER, then det(A? X'In) 0. 1 1 0 0 2 2 0 0 0 0 20 0 0 0 5 g) The number of linearly independent eigenvectors of the matrix is 3. h) If A is an eigenvalue of A, then it is also an eigenvalue of AT. (1) a, d, f, g (2) , b, , f (3) , , f, g (4) , , , f (5) , , f, h (6) , , d, f, h (7) , , d, g, h (8) a, e, f, g, h (9) , b, , , h (10) , , , f, g, h (11) a, d, e, f, g, h (12) b, , d, f, g (13) , b, , , h (14) d, e, f, g, h