Hello everybody I'm not certain with this question.
So if lets say $$ W = L\bigl((1,1,0,-1),\, (0,-1,1,1),\, (3,1,2,-1)\bigr) \subset \mathbb{R}^4; $$ $L$ being the space generated or set of linear combinations of these vectors I want to find the base and the dimension of $W$.
So my thinking is I need to use Gaussian Elimination Matrix and put these $3$ vectors and find the rank which in this case I got $\operatorname{rank} = 2$. So by this the first two columns have pivot and that means that the first two vectors are base for $W$ which means it is a $2$-dimensional matrix.
Is my approach correct? Any feedback is gladly appreciated!