Show that the list $(1,2), (3,5)$ is a basis for $\mathbb R^2$.
In order to show it is a basis, I have show that the list is linearly independent and that the list spans $\mathbb R^2$.
So I understand how to show linear independence (you simply set up a system of equations). However, I am uncertain as to how to show that it spans $\mathbb R^2$. How can you be certain that just by using $(1,2)$ and $(3,5)$ you will be able to produce all $\mathbb R^2$?