Given that (a,b) and (c,d) are vectors in $\displaystyle R^2$ which do not lie on the same line through the origin then prove

1) the span Sp{(a, b), (c, d)} is equal to $\displaystyle R^2$

2) the proper subspaces of $\displaystyle R^2$ are the lines through the origin.

I think I'm pretty close with 1 by showing both sides of the equation are subsets of each other.