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Exercise 2

Avg difficulty 3.0

Which of these subsets of P3\mathcal{P}_{3} are linearly dependent and which are independent?

  • {3−x+9x2,5−6x+3x2,1+1x−5x2}\{\hskip 1.00006pt3-x+9x^{2},5-6x+3x^{2},1+1x-5x^{2}\hskip 1.00006pt\}

  • {−x2,1+4x2}\{\hskip 1.00006pt-x^{2},1+4x^{2}\hskip 1.00006pt\}

  • {2+x+7x2,3−x+2x2,4−3x2}\{\hskip 1.00006pt2+x+7x^{2},3-x+2x^{2},4-3x^{2}\hskip 1.00006pt\}

  • {8+3x+3x2,x+2x2,2+2x+2x2,8−2x+5x2}\{\hskip 1.00006pt8+3x+3x^{2},x+2x^{2},2+2x+2x^{2},8-2x+5x^{2}\hskip 1.00006pt\}

Hefferon, Linear Algebra, Vector Spaces, Definition and Examples, Exercise 2

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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.