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A First Course in Linear Algebra
· Problem B.C10
Vector Spaces — Robert Beezer
Mathematics — Linear Algebra · basis-span
Problem
Find a basis for
⟨
S
⟩
\langle S \rangle
⟨
S
⟩
, where
S
=
{
[
1
3
2
1
]
,
[
1
2
1
1
]
,
[
1
1
0
1
]
,
[
1
2
2
1
]
,
[
3
4
1
3
]
}
.
S = \left\{\begin{bmatrix}1\\3\\2\\1\end{bmatrix},\begin{bmatrix}1\\2\\1\\1\end{bmatrix},\begin{bmatrix}1\\1\\0\\1\end{bmatrix},\begin{bmatrix}1\\2\\2\\1\end{bmatrix},\begin{bmatrix}3\\4\\1\\3\end{bmatrix}\right\}.
S
=
⎩
⎨
⎧
1
3
2
1
,
1
2
1
1
,
1
1
0
1
,
1
2
2
1
,
3
4
1
3
⎭
⎬
⎫
.
Related theory
Change Of Basis And The Change Of Basis Matrix
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