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 =
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
Related questions
Question
![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 =
->](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7410b49b-4737-4519-bf59-ff73aeeb4cca%2Ff475159c-8023-40b6-b00c-293be23b1bcd%2Faahg5zg_processed.png&w=3840&q=75)
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 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7410b49b-4737-4519-bf59-ff73aeeb4cca%2Ff475159c-8023-40b6-b00c-293be23b1bcd%2Fk5mlxld_processed.png&w=3840&q=75)
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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