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)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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.
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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