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Question 5. (a) Diagonalize the matrix S = [1 0 -11 -1 2-1 and calculate A100....
Consider the following matrices 2. .6 6 .9 A2 Ag (a) Diagonalize each matrix by writing...
Consider the following matrices 2. .6 6 .9 A2 Ag (a) Diagonalize each matrix by writing A SAS-1 (b) For each of these three matrices, compute the limit Ak-SNS-1 as k-+ 00 if it exists. (c) Suppose A is an n x n matrix that is diagonalizable (so it has n linearly independent eigenvectors). What must be true for the limit Ak to exist as k → oo? What is needed for Ak-+ O? Justify your answer.
3. ( Find all eigenvalues and eigenvectors of the matrix A= [ 5 | 3 -1]...
3. ( Find all eigenvalues and eigenvectors of the matrix A= [ 5 | 3 -1] and show the eigen- 1 vectors are linearly independent.
2. Consider the matrix 11 2 4 0 0 -1 1 7 0 0 0 6...
2. Consider the matrix 11 2 4 0 0 -1 1 7 0 0 0 6 10 007) Is this matrix diagonalizable? Explain why or why not. 3. Consider the matrix /1 a b 5 0 1 C 3 A = 0 0 1 2 0 0 0 2 For which values of a, b, c E R is A diagonalizable? Justify your answer.
Show that the matrix is not diagonalizable. 2 43 0 21 0 03 STEP 1: Use...
Show that the matrix is not diagonalizable. 2 43 0 21 0 03 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) -- STEP 2: Find the eigenvectors x, and X corresponding to d, and 12, respectively, STEP 3: Since the matrix does not have Select linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
3. Find all the eigenvalues and corresponding eigenspaces for the matrix B = 4. Show that...
3. Find all the eigenvalues and corresponding eigenspaces for the matrix B = 4. Show that the matrix B = 0 1 is not diagonalizable. 0 4] Lo 5. Let 2, and 1, be two distinct eigenvalues of a matrix A (2, # 12). Assume V1, V2 are eigenvectors of A corresponding to 11 and 22 respectively. Prove that V1, V2 are linearly independent.
Show that the matrix is not diagonalizable. 1-42 13 0 02 STEP 1: Use the fact...
Show that the matrix is not diagonalizable. 1-42 13 0 02 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (11.22) = STEP 2: Find the eigenvectors Xi and X2 corresponding to 1, and 12, respectively. X1 = X2 - STEP 3: Since the matrix does not have ---Select-- linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
(1 2 0 1 11. Consider the matrix A = (3 0 1 ) 10 2...
(1 2 0 1 11. Consider the matrix A = (3 0 1 ) 10 2 -1) (a) Are the columns of A are linearly independent? Justify your answer. Is A invertible? (b) Compute factors L and U so that A = LU, with L unit lower triangular and U upper triangular. Please show your work.
linear algebra Explain why the matrix is not diagonalizable. A= 8 0 0 1 8 0...
linear algebra
Explain why the matrix is not diagonalizable. A= 8 0 0 1 8 0 0 0 8 O A is not diagonalizable because it only has one distinct eigenvalue. O A is not diagonalizable because it only has two distinct eigenvalues. O A is not diagonalizable because it only has one linearly independent eigenvector. O A is not diagonalizable because it only has two linearly independent eigenvectors.
Please refer to illustration for question. Diagonalize the matrix A, if possible. That is, find an...
Please refer to illustration for question.
Diagonalize the matrix A, if possible. That is, find an invertible matrix Pand a diagonal matrix D such that A = PDP-1. A = -11 0 6 3 -5 -3 -91 0 4 12 A = 1 LO 0 0 2 0 0 2 0 0 0 9 A= 9 0 -16 0 0 0 16 9 4 1 0 0
Explain why the matrix is not diagonalizable. 600] A = 1 60 0 0 6 O...
Explain why the matrix is not diagonalizable. 600] A = 1 60 0 0 6 O A is not diagonalizable because it only has one distinct eigenvalue. O A is not diagonalizable because it only has two distinct eigenvalues. O A is not diagonalizable because it only has one linearly independent eigenvector. A is not diagonalizable because it only has two linearly independent eigenvectors
Consider the following matrices 2. .6 6 .9 A2 Ag (a) Diagonalize each matrix by writing A SAS-1 (b) For each of these three matrices, compute the limit Ak-SNS-1 as k-+ 00 if it exists. (c) Suppose A is an n x n matrix that is diagonalizable (so it has n linearly independent eigenvectors). What must be true for the limit Ak to exist as k → oo? What is needed for Ak-+ O? Justify your answer.
3. ( Find all eigenvalues and eigenvectors of the matrix A= [ 5 | 3 -1] and show the eigen- 1 vectors are linearly independent.
2. Consider the matrix 11 2 4 0 0 -1 1 7 0 0 0 6 10 007) Is this matrix diagonalizable? Explain why or why not. 3. Consider the matrix /1 a b 5 0 1 C 3 A = 0 0 1 2 0 0 0 2 For which values of a, b, c E R is A diagonalizable? Justify your answer.
Show that the matrix is not diagonalizable. 2 43 0 21 0 03 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) -- STEP 2: Find the eigenvectors x, and X corresponding to d, and 12, respectively, STEP 3: Since the matrix does not have Select linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
3. Find all the eigenvalues and corresponding eigenspaces for the matrix B = 4. Show that the matrix B = 0 1 is not diagonalizable. 0 4] Lo 5. Let 2, and 1, be two distinct eigenvalues of a matrix A (2, # 12). Assume V1, V2 are eigenvectors of A corresponding to 11 and 22 respectively. Prove that V1, V2 are linearly independent.
Show that the matrix is not diagonalizable. 1-42 13 0 02 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (11.22) = STEP 2: Find the eigenvectors Xi and X2 corresponding to 1, and 12, respectively. X1 = X2 - STEP 3: Since the matrix does not have ---Select-- linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
(1 2 0 1 11. Consider the matrix A = (3 0 1 ) 10 2 -1) (a) Are the columns of A are linearly independent? Justify your answer. Is A invertible? (b) Compute factors L and U so that A = LU, with L unit lower triangular and U upper triangular. Please show your work.
linear algebra
Explain why the matrix is not diagonalizable. A= 8 0 0 1 8 0 0 0 8 O A is not diagonalizable because it only has one distinct eigenvalue. O A is not diagonalizable because it only has two distinct eigenvalues. O A is not diagonalizable because it only has one linearly independent eigenvector. O A is not diagonalizable because it only has two linearly independent eigenvectors.
Please refer to illustration for question.
Diagonalize the matrix A, if possible. That is, find an invertible matrix Pand a diagonal matrix D such that A = PDP-1. A = -11 0 6 3 -5 -3 -91 0 4 12 A = 1 LO 0 0 2 0 0 2 0 0 0 9 A= 9 0 -16 0 0 0 16 9 4 1 0 0
Explain why the matrix is not diagonalizable. 600] A = 1 60 0 0 6 O A is not diagonalizable because it only has one distinct eigenvalue. O A is not diagonalizable because it only has two distinct eigenvalues. O A is not diagonalizable because it only has one linearly independent eigenvector. A is not diagonalizable because it only has two linearly independent eigenvectors
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