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Exercise 4

Avg difficulty 3.0

Find the change of basis matrix for each B,D⊆P2B,D\subseteq\mathcal{P}_{2}.

  • (a)  B=⟨1,x,x2⟩,D=⟨x2,1,x⟩B=\langle 1,x,x^{2}\rangle,D=\langle x^{2},1,x\rangle     (b)  B=⟨1,x,x2⟩,D=⟨1,1+x,1+x+x2⟩B=\langle 1,x,x^{2}\rangle,D=\langle 1,1+x,1+x+x^{2}\rangle     (c)  B=⟨2,2x,x2⟩,D=⟨1+x2,1−x2,x+x2⟩B=\langle 2,2x,x^{2}\rangle,D=\langle 1+x^{2},1-x^{2},x+x^{2}\rangle

Hefferon, Linear Algebra, Maps Between Spaces, Changing Representations of Vectors, Exercise 4

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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.