1) Which of the following statements are correct? a) A square matrix A is not invertible...

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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 vị 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) а, b, с, f (3) с, е, f, g (4) а, с, е, f (5) а, с, f, h (6) Ь, с, d, f, h (7) а, с, d, g, h (8) a, e, f, g, h (9) а, b, с, е, h (10) а, с, е, f, g, h (11) a, d, e, f, g, h (12) b, с, d, f, g (13) а, b, с, е, h (14) d, e, f, g, h 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 vị 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) а, b, с, f (3) с, е, f, g (4) а, с, е, f (5) а, с, f, h (6) Ь, с, d, f, h (7) а, с, d, g, h (8) a, e, f, g, h (9) а, b, с, е, h (10) а, с, е, f, g, h (11) a, d, e, f, g, h (12) b, с, d, f, g (13) а, b, с, е, h (14) d, e, f, g, h