So I have a homework question which I am not sure if I am answering correctly. The questions is as follows.

> 
> Determine whether the set is a basis for $\mathcal{R}^3$. If the set isn't a basis, determine if it's linearly independent or spans $\mathcal{R}^3$.
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So I have 4 column vectors
$$\begin{pmatrix} 1\\ -2\\ 3\end{pmatrix},\begin{pmatrix} 0\\ 3\\ -1\\\end{pmatrix}, \begin{pmatrix} 2\\ -1\\ 5\\\end{pmatrix},\begin{pmatrix} 0\\ 0\\ 1\\\end{pmatrix}$$
I combined the vectors into a $3\times4$ matrix and got the RREF of that matrix which is 

$$\begin{pmatrix} 1 \hspace{5pt}0 \hspace{5pt}2 \hspace{5pt}0\\ 0 \hspace{5pt}1 \hspace{5pt}1 \hspace{5pt}0\\ 0 \hspace{5pt}0 \hspace{5pt}0 \hspace{5pt}1\\\end{pmatrix}$$

So what I got from the RREF is that the vectors are not a basis for $\mathcal{R}^3$ since they're not linearly independent. But how do I know if they span $\mathcal{R}^3$? 

I'm having trouble finding good examples where the combined column matrices are of size $n\times m$ instead of size $n \times n$ and that tell me what does the RREF of the matrix actually means.

Thanks for all the help in advance!