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4. [-/1 Points] DETAILS MY NOTES LARLINALG8 7.2.019.SBS. Show that the matrix is not diagonalizable. 2-2 1 20 24 0 3 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (1,2)= =([ STEP 2: Find the eigenvectors X1 and X2 corresponding to λ₁ 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. Need Help? Read It Submit Answer 5. [-/1 Points] DETAILS MY NOTES LARLINALG8 7.2.027. Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R² → R²: T(x, y) = (6x + 3y, 2x + y) B = -> For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not possible, enter IMPOSSIBLE.) 6 -2 -[47] A = -3 1 P = Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal. P-1AP =

4. [-/1 Points] DETAILS MY NOTES LARLINALG8 7.2.019.SBS. Show that the matrix is not diagonalizable. 2-2 1 20 24 0 3 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (1,2)= =([ STEP 2: Find the eigenvectors X1 and X2 corresponding to λ₁ 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. Need Help? Read It Submit Answer 5. [-/1 Points] DETAILS MY NOTES LARLINALG8 7.2.027. Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R² → R²: T(x, y) = (6x + 3y, 2x + y) B = -> For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not possible, enter IMPOSSIBLE.) 6 -2 -[47] A = -3 1 P = Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal. P-1AP =

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CR: Review Exercises
Problem 66CR
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4. [-/1 Points] DETAILS MY NOTES LARLINALG8 7.2.019.SBS. Show that the matrix is not diagonalizable. 2-2 1 20 24 0 3 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (1,2)= =([ STEP 2: Find the eigenvectors X1 and X2 corresponding to λ₁ 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. Need Help? Read It Submit Answer 5. [-/1 Points] DETAILS MY NOTES LARLINALG8 7.2.027. Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R² → R²: T(x, y) = (6x + 3y, 2x + y) B = ->
Transcribed Image Text:4. [-/1 Points] DETAILS MY NOTES LARLINALG8 7.2.019.SBS. Show that the matrix is not diagonalizable. 2-2 1 20 24 0 3 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (1,2)= =([ STEP 2: Find the eigenvectors X1 and X2 corresponding to λ₁ 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. Need Help? Read It Submit Answer 5. [-/1 Points] DETAILS MY NOTES LARLINALG8 7.2.027. Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R² → R²: T(x, y) = (6x + 3y, 2x + y) B = ->
For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not possible, enter IMPOSSIBLE.) 6 -2 -[47] A = -3 1 P = Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal. P-1AP =
Transcribed Image Text:For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not possible, enter IMPOSSIBLE.) 6 -2 -[47] A = -3 1 P = Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal. P-1AP =
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