Home
Random
Log in
Settings
Donate
About Wikiversity
Disclaimers
Search
Q^4/Generated linear subspaces/Equal/1/Exercise
Language
Watch
Edit
We consider in
Q
4
{\displaystyle {}\mathbb {Q} ^{4}}
the
linear subspaces
U
=
⟨
(
3
1
−
5
2
)
,
(
2
−
2
4
−
3
)
,
(
1
0
3
2
)
⟩
{\displaystyle {}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
=
⟨
(
6
−
1
2
1
)
,
(
0
−
2
−
2
−
7
)
,
(
9
2
−
1
10
)
⟩
.
{\displaystyle {}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
{\displaystyle {}U=W}
.
Create a solution