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Exercise 6

Avg difficulty 3.0

Which of these are members of the span [{cos⁡2x,sin⁡2x}][\text{$\{\hskip 1.00006pt\cos^{2}x,\sin^{2}x\hskip 1.00006pt\}$}] in the vector space of real-valued functions of one real variable?

  • (a)  f(x)=1f(x)=1     (b)  f(x)=3+x2f(x)=3+x^{2}     (c)  f(x)=sin⁡xf(x)=\sin x     (d)  f(x)=cos⁡(2x)f(x)=\cos(2x)

Hefferon, Linear Algebra, Vector Spaces, Subspaces and Spanning Sets, Exercise 6

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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.