Verifying Linear Independence I saw the following question from M. Artin's book, Algebra. 
I simply need to show the the functions $\cos x$, $\sin x$ and $e^x$ are independent. I have no idea how to show their independence. 
Any help is appreciated but hints are appreciated more than the answer itself. If only the method of proving that the three scalars will identically equal to $0$ is mentioned, I'll be grateful. 

Functions are dependent if they are linear combinations of each other, i.e. if there exists some $\alpha, \beta,\gamma$ such that the function $f=\alpha \cos + \beta\sin + \gamma \exp$ is zero.
But what does it mean for $f$ to be "zero"? What is the zero vector in the space of all functions? Well, you probably know that that's the function that maps **all ** values of $x$ to $0$.
So, you now need to find $\alpha, \beta, \gamma$ such that $\alpha\cos x + \beta\sin x + \gamma e^x$ is true for all real values $x$!
