Q^4/Generated linear subspaces/Equal/1/Exercise

We consider in ${}\mathbb {Q} ^{4}$ the linear subspaces

${}U=\langle {\begin{pmatrix}3\\1\\-5\\2\end{pmatrix}},{\begin{pmatrix}2\\-2\\4\\-3\end{pmatrix}},{\begin{pmatrix}1\\0\\3\\2\end{pmatrix}}\rangle \,$

and

${}W=\langle {\begin{pmatrix}6\\-1\\2\\1\end{pmatrix}},{\begin{pmatrix}0\\-2\\-2\\-7\end{pmatrix}},{\begin{pmatrix}9\\2\\-1\\10\end{pmatrix}}\rangle \,.$

Show that

${}U=W$.

Create a solution