By using appropriate identities, where required, determine if the following set of vectors in F(-infinity, infinity) is linearly dependent: $6, 3(\sin^2(x)), 2(\cos^2(x))$.
So I try to multiple by scalars but since there is little to work with I am stuck on how to set up a matrix to find the solution to a homogeneous system of the scalars. I know that sin squared x plus cos squared x is 1. I believe that is the way to do it. Hmmmm.... Not used to this kind of problem though did the other ones guess I don't understand the whole idea perfectly. Any help would be appreciated, thank you!!!!!
I think it's easier to just give it a hard look and come up with some scalars:
$-1\cdot 6 + 2\cdot(3\sin^2(x)) + 3\cdot(2\cos^2(x))=9$.
My thought process was "how can I find a common 'denominator' so that the $\sin^2$ and $\cos^2$ can be replaced by $1$?" That you had $6$ as a constant function, and that it is $2\cdot 3$, I think sort of gives away that this how you were intended to find a linear dependence.