Show that $\mathbf{v}_1=(1,2,0,-1)^T, \mathbf{v}_2=(-3,1,1,-1)^T, \mathbf{v}_3=(2,0,-4,3)^T$ and $\mathbf{w}_1=(3,2,-4,2)^T, \mathbf{w}_2=(2,3,-7,4)^T, \mathbf{w}_3=(0,3,-3,1)^T$ are two bases for the same three-dimensional subspace $V \subset \mathbb{R}^4$.