Consider the matrix A = 1. Use the characteristic polynomial to find the eigenvalues of A. Call them X₁ and ₂. 2. Find an eigenvector for each eigenvalue. That means, find nonzero vectors ₁ and 2 such that A₁ A₁₁ and A₂ = λ₂0¹₂. =
Consider the matrix A = 1. Use the characteristic polynomial to find the eigenvalues of A. Call them X₁ and ₂. 2. Find an eigenvector for each eigenvalue. That means, find nonzero vectors ₁ and 2 such that A₁ A₁₁ and A₂ = λ₂0¹₂. =
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![[3]
1. Use the characteristic polynomial to find the eigenvalues of A. Call them A₁ and A₂.
Consider the matrix A=
2. Find an eigenvector for each eigenvalue. That means, find nonzero vectors ₁ and 2 such that.
A₁ A₁₁ and Av₂ = √₂0¹₂.
3. Let P=[12]. Use the formula for the inverse of a 2 x 2 matrix to calculate P-¹.
4. Carefully calculate P-¹AP. What do you notice? Hint: you should not get A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a7e99bb-b9c4-47fa-9081-3b9aeb6b94e4%2Fa3e01b4e-1642-4fa8-98e4-50ff06c3b85c%2F73lh5lh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[3]
1. Use the characteristic polynomial to find the eigenvalues of A. Call them A₁ and A₂.
Consider the matrix A=
2. Find an eigenvector for each eigenvalue. That means, find nonzero vectors ₁ and 2 such that.
A₁ A₁₁ and Av₂ = √₂0¹₂.
3. Let P=[12]. Use the formula for the inverse of a 2 x 2 matrix to calculate P-¹.
4. Carefully calculate P-¹AP. What do you notice? Hint: you should not get A.
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