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Exercise 8

Avg difficulty 3.0

What is the dimension of the span of the set {cos⁡2θ,sin⁡2θ,cos⁡2θ,sin⁡2θ}\{\hskip 1.00006pt\cos^{2}\theta,\sin^{2}\theta,\cos 2\theta,\sin 2\theta\hskip 1.00006pt\}? This span is a subspace of the space of all real-valued functions of one real variable.

Hefferon, Linear Algebra, Vector Spaces, Dimension, Exercise 8

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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.