Consider the following. -2 10 0 1 -3 [] 20 04 4-2 4 (a) Verify that A is diagonalizable by computing P-¹AP. A = P-¹AP = 000 12 2 (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. (2₁₁ 2₂₁23) =

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 15CR: For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of...
icon
Related questions
Question
Consider the following.
-2 10
0
20
A =
0 1 -3
0 4 0
12 2
4-2 4
(a) Verify that A is diagonalizable by computing P-¹AP.
P-¹AP =
;]P=[i
(2₁₁2₂₁23) =
↓↑
(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.
Transcribed Image Text:Consider the following. -2 10 0 20 A = 0 1 -3 0 4 0 12 2 4-2 4 (a) Verify that A is diagonalizable by computing P-¹AP. P-¹AP = ;]P=[i (2₁₁2₂₁23) = ↓↑ (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.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage