(3) Let A, B, and C be square matrices of the same order. Which of the following statements is false? (a) If A is similar to B, then A and B have the same set of eigenvalues. (b) If A is similar to B, then A" is similar to B" for all positive integers n. (c) There exist matrices A, B, and C such that A is similar to B, and B is similar to C, but A is not similar to C. (d) If A is similar to B, then det(A) = det(B). (1 mark)
(3) Let A, B, and C be square matrices of the same order. Which of the following statements is false? (a) If A is similar to B, then A and B have the same set of eigenvalues. (b) If A is similar to B, then A" is similar to B" for all positive integers n. (c) There exist matrices A, B, and C such that A is similar to B, and B is similar to C, but A is not similar to C. (d) If A is similar to B, then det(A) = det(B). (1 mark)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please answer as fast as possible
![(3) Let A, B, and C be square matrices of the same order. Which of the following
statements is false?
(a) If A is similar to B, then A and B have the same set of eigenvalues.
(b) If A is similar to B, then A" is similar to B" for all positive integers n.
(c) There exist matrices A, B, and C such that A is similar to B, and B is similar
to C, but A is not similar to C.
(d) If A is similar to B, then det(A) = det(B).
(1 mark)
%3D
(4) Let
1 10
A = 0 2 0
0 03
and B = A' + 4A? + 31. The set of eigenvalues of B is
(a) {8, 35, 120}
(b) {6, 35, 40}
(c) {6, 32, 20}
(d) {8, 32. 80}
(1 mark)
(5) Let B and B' be ordered bases of a finite dimensional vector space V. Let P be the
transition matrix from B to B'. Choose the correct statement:
(a) P will always be a symmetric matrix.
(b) P will always be a diagonal matrix.
(c) P will alwways be a singular matrix
(d) None of the above statements is correct.
(1 mark)
(6) Let A be an 3 x 3 matrix with real entries. If A is similar to the diagonal matrix
D =
(1 mark)
then set of eigenvalucs of A is
(a) (1}
(b) {2}
(c) {3}
(d) (1.2,3}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4ca600e-53d7-4fe3-b654-ccc97c85b461%2Fa61541dc-9511-4ca0-99dd-0562795a7bae%2Fcbnppn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(3) Let A, B, and C be square matrices of the same order. Which of the following
statements is false?
(a) If A is similar to B, then A and B have the same set of eigenvalues.
(b) If A is similar to B, then A" is similar to B" for all positive integers n.
(c) There exist matrices A, B, and C such that A is similar to B, and B is similar
to C, but A is not similar to C.
(d) If A is similar to B, then det(A) = det(B).
(1 mark)
%3D
(4) Let
1 10
A = 0 2 0
0 03
and B = A' + 4A? + 31. The set of eigenvalues of B is
(a) {8, 35, 120}
(b) {6, 35, 40}
(c) {6, 32, 20}
(d) {8, 32. 80}
(1 mark)
(5) Let B and B' be ordered bases of a finite dimensional vector space V. Let P be the
transition matrix from B to B'. Choose the correct statement:
(a) P will always be a symmetric matrix.
(b) P will always be a diagonal matrix.
(c) P will alwways be a singular matrix
(d) None of the above statements is correct.
(1 mark)
(6) Let A be an 3 x 3 matrix with real entries. If A is similar to the diagonal matrix
D =
(1 mark)
then set of eigenvalucs of A is
(a) (1}
(b) {2}
(c) {3}
(d) (1.2,3}
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