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Linear Algebra and Its Applications
· Problem 2.4.12
Vector Spaces — Gilbert Strang
Mathematics · four-fundamental-subspaces
Problem
Find the rank of
A
A
A
and write the matrix as
A
=
u
v
T
A = uv^T
A
=
u
v
T
:
A
=
[
1
0
0
3
0
0
0
0
2
0
0
6
]
and
A
=
[
2
−
2
6
−
6
]
.
A = \begin{bmatrix} 1 & 0 & 0 & 3 \\ 0 & 0 & 0 & 0 \\ 2 & 0 & 0 & 6 \end{bmatrix} \quad \text{and} \quad A = \begin{bmatrix} 2 & -2 \\ 6 & -6 \end{bmatrix}.
A
=
1
0
2
0
0
0
0
0
0
3
0
6
and
A
=
[
2
6
−
2
−
6
]
.
Related theory
The Four Fundamental Subspaces
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