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Linear Algebra and Its Applications
· Problem 2.4.38
Vector Spaces — Gilbert Strang
Mathematics · four-fundamental-subspaces
Problem
If
A
B
=
0
AB = 0
A
B
=
0
, the columns of
B
B
B
are in the nullspace of
A
A
A
. If those vectors are in
R
n
\mathbf{R}^n
R
n
, prove that
rank
(
A
)
+
rank
(
B
)
≤
n
\text{rank}(A) + \text{rank}(B) \leq n
rank
(
A
)
+
rank
(
B
)
≤
n
.
Related theory
The Four Fundamental Subspaces
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