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Back to Eigenvalues and Eigenvectors

Exercise 8

Avg difficulty 3.0

Let t ⁣:P2→P2t\colon\mathcal{P}_{2}\to\mathcal{P}_{2} be this linear map.

a0+a1x+a2x2↦(5a0+6a1+2a2)−(a1+8a2)x+(a0−2a2)x2a_{0}+a_{1}x+a_{2}x^{2}\mapsto(5a_{0}+6a_{1}+2a_{2})-(a_{1}+8a_{2})x+(a_{0}-2a_{2})x^{2}

Find its eigenvalues and the associated eigenvectors.

Hefferon, Linear Algebra, Similarity, Eigenvalues and Eigenvectors, Exercise 8

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.