![(4) (15 marks) Repeat the Question 2 for the following matrices -3 4 0] 0 0 A -2 30 B 0 -1 0 -8 8 1 0 0 1 ū= 10 = > 3](http://img.homeworklib.com/questions/f7a667a0-edfd-11ea-8299-b91c73ab7cb7.png?x-oss-process=image/resize,w_560)
Homework Answers
![(VI) b= [] a [3]*1 [i]+c[] 2atb atb +4+с then _26+6=1 [band szatb=1 a+b=0>92-6 How → a=1 and 4a+C=3 Carl :. b = to) +(1) = 1](http://img.homeworklib.com/questions/1abef4b0-edff-11ea-ac6c-192d8bce3900.png?x-oss-process=image/resize,w_560)
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(4) (15 marks) Repeat the Question 2 for the following matrices -3 4 0] 0 0...
(4) (15 marks) Repeat the Question 2 for the following matrices -3 4 0] 0 0...
(4) (15 marks) Repeat the Question 2 for the following matrices -3 4 0] 0 0 A -2 30 B 0 -1 0 -8 8 1 0 0 1 ū= 10 = > 3 (I) (2 mark) Find the characteristic polynomial of matrix A. (II) (1 mark) Find eigenvalues of the matrix A. III) (2 mark) Find a basis for the eigenspaces of matrix A. IV) (1 mark) What is the algebraic and geometric multiplicities of its eigenvalues. (V) (2...
(2) (15 marks) Consider matrices 2 A= and B= 8 12 -2 3 b= = []...
(2) (15 marks) Consider matrices 2 A= and B= 8 12 -2 3 b= = [] (VI) (2 marks) Find A16 by writing 7 as linear combination of eigenvectors of A. (VII) (2 marks) Find a formula for Ak for all non-negative integers k. (Can k be a negative integer?) (VIII) (1 mark) Use (VII) to find Alº7 and compare it with what you found in (VI). (IX) (2 mark) Is A similar to B? If yes, find an invertible...
8. (a) For what values of a, b, and c can the matrix A below be...
8. (a) For what values of a, b, and c can the matrix A below be diagonalized? 2 marks 0 a 1 0 =10 0 0 c b) Let A be an n xn matrix. In class, we showed that if R" admits a basis of eigenvectors of A, then there is an invertible atrix P such that P- AP is diagonal (i.e., is zero everywhere apart from along the main diagonal) Show, conversely, that if there exists an invertible...
2. [-12 Points) DETAILS LARLINALG8 7.2.005. Consider the following. -4 20 0 1 -3 A =...
2. [-12 Points) DETAILS LARLINALG8 7.2.005. Consider the following. -4 20 0 1 -3 A = 040 P= 04 0 4 0 2 1 2 2 (a) Verify that A is diagonalizable by computing p-AP. p-1AP = 11 (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (91, 12, 13)...
Please help and explain all steps 9 Marks [5 0 0 1 8. Let A= 10...
Please help and explain all steps
9 Marks [5 0 0 1 8. Let A= 10 3 [0 0 -2] (a) Find all eigenvalues of A and their corresponding eigenvectors. (b) Is A diagonalizable? If so, find a matrix P and diagonal matrix D such that P-1AP = D.
Let A = -2 -2 6 1 -2. -2 co (a) Compute eigenvalues and corresponding eigenvectors...
Let A = -2 -2 6 1 -2. -2 co (a) Compute eigenvalues and corresponding eigenvectors of A. (b) Find an invertible matrix P such that P-1AP is diagonal. (c) Find an orthogonal matrix Q (that is QT = Q-1 ) such that QTAQ is diagonal (d) Compute e At
Let A = 4 0 0 2 1 2 1 2 1 (a)(4 marks) Find the...
Let A = 4 0 0 2 1 2 1 2 1 (a)(4 marks) Find the eigenvalues of A. (b)(2 marks) Explain without any more calculations that A is diagonalisable. ((7 marks) Find three linearly independent eigenvectors of the matrix A. (d)(2 marks) Write an invertible matrix P such that -100 P-AP=0 40 0 0 3
a casute de 8. Consider the 2 x 2 real matrices A = masina - E...
a casute de 8. Consider the 2 x 2 real matrices A = masina - E |---B and D (a) (2 marks) Show that A and D have the same eigenvalues. (b) (4 marks) Find an eigenbasis of A. (c) (3 marks) Find an invertible matrix P satisfying P-1AP = D.
Let A be a diagonalizable n x n matrix and let P be an invertible n...
Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P-1AP is the diagonal form of A. Prove that Ak = Pekp-1, where k is a positive integer. Use the result above to find the indicated power of A. 0-2 02-2 3 0 -3 ,45 A5 = 11
Let A be a diagonalizable n × n matrix and let P be an invertible n...
Let A be a diagonalizable n × n matrix and let P be an invertible n × n matrix such that B = P−1AP is the diagonal form of A. Prove that Ak = PBkP−1, where k is a positive integer. Use the result above to find the indicated power of A. A = −4 0 4 −3 −1 4 −6 0 6 , A5
(4) (15 marks) Repeat the Question 2 for the following matrices -3 4 0] 0 0 A -2 30 B 0 -1 0 -8 8 1 0 0 1 ū= 10 = > 3 (I) (2 mark) Find the characteristic polynomial of matrix A. (II) (1 mark) Find eigenvalues of the matrix A. III) (2 mark) Find a basis for the eigenspaces of matrix A. IV) (1 mark) What is the algebraic and geometric multiplicities of its eigenvalues. (V) (2...
(2) (15 marks) Consider matrices 2 A= and B= 8 12 -2 3 b= = [] (VI) (2 marks) Find A16 by writing 7 as linear combination of eigenvectors of A. (VII) (2 marks) Find a formula for Ak for all non-negative integers k. (Can k be a negative integer?) (VIII) (1 mark) Use (VII) to find Alº7 and compare it with what you found in (VI). (IX) (2 mark) Is A similar to B? If yes, find an invertible...
8. (a) For what values of a, b, and c can the matrix A below be diagonalized? 2 marks 0 a 1 0 =10 0 0 c b) Let A be an n xn matrix. In class, we showed that if R" admits a basis of eigenvectors of A, then there is an invertible atrix P such that P- AP is diagonal (i.e., is zero everywhere apart from along the main diagonal) Show, conversely, that if there exists an invertible...
2. [-12 Points) DETAILS LARLINALG8 7.2.005. Consider the following. -4 20 0 1 -3 A = 040 P= 04 0 4 0 2 1 2 2 (a) Verify that A is diagonalizable by computing p-AP. p-1AP = 11 (b) Use the result of part (a) and the theorem below to find the eigenvalues of A. Similar Matrices Have the Same Eigenvalues If A and B are similar n x n matrices, then they have the same eigenvalues. (91, 12, 13)...
Please help and explain all steps
9 Marks [5 0 0 1 8. Let A= 10 3 [0 0 -2] (a) Find all eigenvalues of A and their corresponding eigenvectors. (b) Is A diagonalizable? If so, find a matrix P and diagonal matrix D such that P-1AP = D.
Let A = -2 -2 6 1 -2. -2 co (a) Compute eigenvalues and corresponding eigenvectors of A. (b) Find an invertible matrix P such that P-1AP is diagonal. (c) Find an orthogonal matrix Q (that is QT = Q-1 ) such that QTAQ is diagonal (d) Compute e At
Let A = 4 0 0 2 1 2 1 2 1 (a)(4 marks) Find the eigenvalues of A. (b)(2 marks) Explain without any more calculations that A is diagonalisable. ((7 marks) Find three linearly independent eigenvectors of the matrix A. (d)(2 marks) Write an invertible matrix P such that -100 P-AP=0 40 0 0 3
a casute de 8. Consider the 2 x 2 real matrices A = masina - E |---B and D (a) (2 marks) Show that A and D have the same eigenvalues. (b) (4 marks) Find an eigenbasis of A. (c) (3 marks) Find an invertible matrix P satisfying P-1AP = D.
Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P-1AP is the diagonal form of A. Prove that Ak = Pekp-1, where k is a positive integer. Use the result above to find the indicated power of A. 0-2 02-2 3 0 -3 ,45 A5 = 11
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