Question: Prove that the list (x^3, sin(x), cos(x)) is linearly independent in V (V being the vector space of real-valued functions. In other words... common everyday math)(adsbygoogle = window.adsbygoogle || []).push({});

They're linearly independent, its pretty obvious. The issue is -- proving rigorously. This is not for an assignment, its for exam prep. (Friday)

Started by setting them as a linear combination:

c1*x^3 + c2*sin(x) + c3*cos(x) = 0 and trying to prove that ALL the coefficients need to be zero. But, nothing's rigorous enough.

Any ideas?

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# Prove that the list (x^3, sin(x), cos(x)) is linearly independent in V

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