Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
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Chapter B, Problem 47E
To determine
The eigenvalues and eigenvectors of the given matrix.
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(1 point) For which value of k does the matrix
k
A =
5
have one real eigenvalue of multiplicity 2?
k =
%3D
2 4
What are the eigenvalues of the matrix
1 2
Select one:
O A 3,2
O B.2,2
O C. 0,-4
O D.0.4
O E. 2
7. (4 points). Show that if 1 = 4 is an eigenvalue of an n x n matrix T , then 16 is an eigen-
value of the matrix T².
Chapter B Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
Ch. B - Prob. 1ECh. B - Prob. 2ECh. B - Prob. 3ECh. B - Prob. 4ECh. B - Prob. 5ECh. B - Prob. 6ECh. B - Prob. 7ECh. B - Prob. 8ECh. B - Prob. 9ECh. B - Prob. 10E
Ch. B - Prob. 11ECh. B - Prob. 12ECh. B - Prob. 13ECh. B - Prob. 14ECh. B - In Problems 1522 determine whether the given...Ch. B - Prob. 16ECh. B - Prob. 17ECh. B - Prob. 18ECh. B - Prob. 19ECh. B - Prob. 20ECh. B - Prob. 21ECh. B - In Problems 1522 determine whether the given...Ch. B - Prob. 23ECh. B - Prob. 24ECh. B - Prob. 25ECh. B - Prob. 26ECh. B - Prob. 27ECh. B - Prob. 28ECh. B - Prob. 29ECh. B - Prob. 30ECh. B - Prob. 31ECh. B - Prob. 32ECh. B - Prob. 33ECh. B - Prob. 34ECh. B - Prob. 35ECh. B - Prob. 36ECh. B - Prob. 37ECh. B - Prob. 38ECh. B - Prob. 39ECh. B - Prob. 40ECh. B - Prob. 41ECh. B - Prob. 42ECh. B - Prob. 43ECh. B - Prob. 44ECh. B - Prob. 45ECh. B - Prob. 46ECh. B - Prob. 47ECh. B - Prob. 48ECh. B - Prob. 49ECh. B - Prob. 50ECh. B - Prob. 51ECh. B - Prob. 52ECh. B - Prob. 53ECh. B - Prob. 54ECh. B - Prob. 55ECh. B - Prob. 56ECh. B - Prob. 57ECh. B - Prob. 58ECh. B - Prob. 59ECh. B - Prob. 60ECh. B - Prob. 61ECh. B - Prob. 62E
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- 5. Find the generalized eigenvectors of the following matrix: -2 1. A = -2 1 -2 In one paragraph (about 200 – 300 words) explain your thinking.arrow_forwardQuestion 6. Which are eigenvalues of the matrix3 2 50 2 30 1 4a) 2b) 3c) 5d) 0arrow_forwardEx. 1 Find the eigenvalues A = and eigenvectors of the matrix. -4.0 4.01 -1.6 1.21arrow_forward
- 3 6. #5. Let A = -- 2 3 What are the eigenvalues of A? 4 0. (A)3, – 2,4 (B) – 3, 2, - 4 (C) 1, 6,7 (D) 3, 4,7 (E) – 2, – 3,5arrow_forward21. Working Backwards Find a matrix with eigenvalues 2, = 1, 12 = -1, and corresponding eigenvectors and v2arrow_forwardhas two distinct eigenvalues if and only if 9. The matrix A = k > Add Work > Next Questionarrow_forward
- 2 1 -1 Find an eigenvector of the matrix – 48 – 12 10 corresponding to the eigenvalue 1 = – 4. - 18 - 3 1 |arrow_forward10. Which of the following can be the main diagonal for the diagonal matrix D of a matrix A with eigenvalues 1, 2, and 4? (ii) (iii) (iv) (v) (vi) diag(1, 2, 4) diag(1, 1, 1) diag(2, 1, 4) diag(4, 2, 1) diag(2, 4, 1) diag(4, 4, 4) a) (i) only d) (i), (iii), (iv), and (v) only b) (i) and (iv) only e) (ii) and (vi) only c) (i), (ii), and (vi) only f) none of thesearrow_forward5. Find a 3x3 symmetric matrix that has eigenvalues A₁ = 1, A₂= 3, A3 = 5 and corresponding (-¹₁). ₂ = ( ¹). ₁ = (¹) , , K₂ eigenvectors K₁ =arrow_forward
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