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Exercise 12

Avg difficulty 3.0

Decide if each is a basis for P2\mathcal{P}_{2}.

  • (a)  {1,x2,x2−x}\{\hskip 1.00006pt1,x^{2},x^{2}-x\hskip 1.00006pt\}     (b)  {x2+x,x2−x}\{\hskip 1.00006ptx^{2}+x,x^{2}-x\hskip 1.00006pt\}     (c)  {2x2+x+1,2x+1,2}\{\hskip 1.00006pt2x^{2}+x+1,2x+1,2\hskip 1.00006pt\}     (d)  {3x2,−1,3x,x2−x}\{\hskip 1.00006pt3x^{2},-1,3x,x^{2}-x\hskip 1.00006pt\}

Hefferon, Linear Algebra, Vector Spaces, Dimension, Exercise 12

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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.