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Exercise 17

Avg difficulty 3.0

Consider 2+4x2,1+3x2,1+5x2∈P22+4x^{2},1+3x^{2},1+5x^{2}\in\mathcal{P}_{2}.

  • Find a linear relationship among the three.

  • Represent them with respect to B=⟨1−x,1+x,x2⟩B=\langle 1-x,1+x,x^{2}\rangle.

  • Check that the same linear relationship holds among the representations, as in Lemma 1.18.

Hefferon, Linear Algebra, Vector Spaces, Basis, Exercise 17

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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.