5. Let A be a (3×3)-matrix with the characteristic polynomial pA(x) = (2 – x)(x² + 1– a²) for some a E R. (a) Find the value(s) a such that A is not invertible. (b) Give an example of such matrix A with at most 4 nonzero entries.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
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Please answer 5a and b

5. Let A be a (3×3)-matrix with the characteristic polynomial pa(x) = (2 – x)(x² + 1 – a²) for
some a E R.
(a) Find the value(s) a such that A is not invertible.
(b) Give an example of such matrix A with at most 4 nonzero entries.
Transcribed Image Text:5. Let A be a (3×3)-matrix with the characteristic polynomial pa(x) = (2 – x)(x² + 1 – a²) for some a E R. (a) Find the value(s) a such that A is not invertible. (b) Give an example of such matrix A with at most 4 nonzero entries.
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