1. (a) Determine the characteristic polynomial and eigenvalues for 0. A = |-1 1 -1 3 (b) Determine the eigenspaces corresponding to the eigenvalues of A. (Write them as spans of vectors.) (c) Is A diagonalizable? Explain how you know, based on what you did in (a) and (b).

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: λ is an eigen value of a matrix A if  detA-λI=0where I is identity matrix of order same as of A.

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A: Please note that as per bartleby guidelines, I can answer only one question.

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A: A can be diagonalized if there exists an invertible matrix P and diagonal matrix D such that A=PDP-1…

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