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Linear Algebra and Its Applications
· Problem 2.4.32
Vector Spaces — Gilbert Strang
Mathematics · four-fundamental-subspaces
Problem
Describe the four subspaces of
R
3
\mathbf{R}^3
R
3
associated with
A
=
[
0
1
0
0
0
1
0
0
0
]
and
I
+
A
=
[
1
1
0
0
1
1
0
0
1
]
.
A = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{bmatrix} \quad \text{and} \quad I+A = \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}.
A
=
0
0
0
1
0
0
0
1
0
and
I
+
A
=
1
0
0
1
1
0
0
1
1
.
Related theory
The Four Fundamental Subspaces
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