Spanning $\Bbb{R}^2$ Vector Space [duplicate]

We need to break this problem into two parts.

1. If ${v_1,v_2}$ are linearly dependent then they do not span $\mathbb{R}^2$
2. If $v_1,v_2$ are linearly independent then they do span $\mathbb{R}^2$

For the first part ask yourself what does it mean for two vectors to be linearly dependent? How will the span look in this case?

For part two you need to explain why every vector in $\mathbb{R}^2$ will be in the span of $v_1$ and $v_2$. In other words, you need to explain why for every vector $v \in \mathbb{R}^2$ we can solve the equation $v = av_1 +bv_2$. Do you know how to solve an equation like this? They should have taught you how to do this in class. You need to explain why you know your method will work.