Linear Algebra Quiz
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VECTOR SPACES & SUBSPACES
Question 1
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Consider the matrix
A
=
(
1
3
5
−
1
−
1
−
2
−
5
4
0
1
0
3
)
A = \begin{pmatrix} 1 & 3 & 5 & -1 \\ -1 & -2 & -5 & 4 \\ 0 & 1 & 0 & 3 \end{pmatrix}
A
=
1
−
1
0
3
−
2
1
5
−
5
0
−
1
4
3
. Which of the following sets forms a basis for the column space of
A
A
A
?
A
{
(
1
0
0
)
,
(
3
1
0
)
}
\{\begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix}\}
{
1
0
0
,
3
1
0
}
B
{
(
1
3
5
−
1
)
,
(
−
1
−
2
−
5
4
)
}
\{\begin{pmatrix} 1 \\ 3 \\ 5 \\ -1 \end{pmatrix}, \begin{pmatrix} -1 \\ -2 \\ -5 \\ 4 \end{pmatrix}\}
{
1
3
5
−
1
,
−
1
−
2
−
5
4
}
C
{
(
1
−
1
0
)
,
(
3
−
2
1
)
}
\{\begin{pmatrix} 1 \\ -1 \\ 0 \end{pmatrix}, \begin{pmatrix} 3 \\ -2 \\ 1 \end{pmatrix}\}
{
1
−
1
0
,
3
−
2
1
}
D
{
(
1
−
1
0
)
,
(
3
−
2
1
)
,
(
5
−
5
0
)
,
(
−
1
4
3
)
}
\{\begin{pmatrix} 1 \\ -1 \\ 0 \end{pmatrix}, \begin{pmatrix} 3 \\ -2 \\ 1 \end{pmatrix}, \begin{pmatrix} 5 \\ -5 \\ 0 \end{pmatrix}, \begin{pmatrix} -1 \\ 4 \\ 3 \end{pmatrix}\}
{
1
−
1
0
,
3
−
2
1
,
5
−
5
0
,
−
1
4
3
}
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