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) 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?