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In the vector space of real-valued functions
determine if the following set S is linearly independent.
S ={sin2 x, cos2 x, 2}
In the vector space of real-valued functions F =
belongs to book: A First Course in Linear Algebra|Robert A. Beezer|| Chapter number:4| Question number:C24
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Physics
One of the fundamental identities of trigonometry is sin2(x) + cos2(x) = 1. Thus, we have a dependence relation 2(sin2 x) + 2(cos2 x) + (−1)(2) = 0, and the set is linearly dependent.
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