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Linear Algebra and Its Applications
· Problem 3.1.51
Orthogonality — Gilbert Strang
Mathematics · perpendicular-columns-rows
Problem
Suppose
A
A
A
is 3 by 4,
B
B
B
is 4 by 5, and
A
B
=
0
AB = 0
A
B
=
0
. Prove
rank
(
A
)
+
rank
(
B
)
≤
4
\text{rank}(A) + \text{rank}(B) \leq 4
rank
(
A
)
+
rank
(
B
)
≤
4
.
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