Consider the following. 1 2₂ = A = (a) Compute the characteristic polynomial of A. det(A-AI) = -2³ +22² + 192-20 22= 0 0 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) 46 23= 10 4 1 05 has eigenspace span has eigenspace span has eigenspace span (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A₁ has algebraic multiplicity and geometric multiplicity ₂ has algebraic multiplicity and geometric multiplicity 3 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)

Q: What is the relationship between the characteristic polynomial and the eigenvalues of A?

A: Here. We have to find the relationship between eigenvalues and characteristics polynomial.

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A: Here we have to verify that λi  is an eigenvalue of A and that xi is a corresponding eigenvector .

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Q: Exercise: Let A be an invertible n x n matrix. Suppose that u ER" is an eigenvector of A with…

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Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. 2, = 5, x, = (1, 2,…

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Q: Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector. 2 = -11, x, = (1,…

A: To verify that given eigenvalues and eigenvectors are belongs to the given matrix A.

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Q: 2. Without using Sage, find • the characteristic polynomial the eigenvalues (include the…

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

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