Find the dimension of the subspace W {\displaystyle W} in R 5 {\displaystyle \mathbb {R} ^{5}} spanned by the following three vectors
v 1 = [ 3 1 1 0 0 ] , v 2 = [ − 1 2 1 0 0 ] , v 3 = [ − 1 / 2 − 2 7 / 2 0 0 ] . {\displaystyle {\bf {v}}_{1}={\begin{bmatrix}3\\1\\1\\0\\0\end{bmatrix}},\;{\bf {v}}_{2}={\begin{bmatrix}-1\\2\\1\\0\\0\end{bmatrix}},\;{\bf {v}}_{3}={\begin{bmatrix}-1/2\\-2\\7/2\\0\\0\end{bmatrix}}.}
in 
spanned by the following three vectors
