(1 Which of the following statements are correct? a) A square matrix A is not invertible if and only if ) = 0 is an eigenvalue of A. b) If v1 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 of A = 8 e) Let A be an n × n matrix. If det(A – AIn) = 0 for some A E R, then det(A² – \²I„) 7 0. f) Suppose A is a 3 x 3 matrix having eigenvalues –1,1,2. Ak is diagonalizable for any integer k > 0. [1 1 0 o' 2 20 0 is 3. 0 0 2 0 g) The number of linearly independent eigenvectors of the matrix 0 0 0 5 h) If A is an eigenvalue of A, then it is also an eigenvalue of AT. (Submit the corresponding number without parentheses.) (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) а, е, f, g. h (9) а, b, с, e, 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 ) = 0 is an eigenvalue of A. b) If v1 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 of A = 8 e) Let A be an n × n matrix. If det(A – AIn) = 0 for some A E R, then det(A² – \²I„) 7 0. f) Suppose A is a 3 x 3 matrix having eigenvalues –1,1,2. Ak is diagonalizable for any integer k > 0. [1 1 0 o' 2 20 0 is 3. 0 0 2 0 g) The number of linearly independent eigenvectors of the matrix 0 0 0 5 h) If A is an eigenvalue of A, then it is also an eigenvalue of AT. (Submit the corresponding number without parentheses.) (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) а, е, f, g. h (9) а, b, с, e, 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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

(1 Which of the following statements are correct?
a) A square matrix A is not invertible if and only if ) = 0 is an eigenvalue of A.
b) If v1 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 of A =
8
e) Let A be an n × n matrix. If det(A – AIn) = 0 for some A E R, then det(A² – \²I„) 7 0.
f) Suppose A is a 3 x 3 matrix having eigenvalues –1,1,2. Ak is diagonalizable for any integer
k > 0.
[1 1 0 o'
2 20 0
is 3.
0 0 2 0
g) The number of linearly independent eigenvectors of the matrix
0 0 0 5
h) If A is an eigenvalue of A, then it is also an eigenvalue of AT.
(Submit the corresponding number without parentheses.)
(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) а, е, f, g. h
(9) а, b, с, e, 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

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