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VTRMC
2005 VTRMC
Problem 7
Problem 7
Part of
2005 VTRMC
Problems
(1)
tranpose, 5x10 matrices
Source: VTRMC 2005 P7
6/10/2021
Let
A
A
A
be a
5
×
10
5\times10
5
×
10
matrix with real entries, and let
A
T
A^{\text T}
A
T
denote its transpose. Suppose every
5
×
1
5\times1
5
×
1
matrix with real entries can be written in the form
A
u
A\mathbf u
A
u
where
u
\mathbf u
u
is a
10
×
1
10\times1
10
×
1
matrix with real entries. Prove that every
5
×
1
5\times1
5
×
1
matrix with real entries can be written in the form
A
A
T
v
AA^{\text T}\mathbf v
A
A
T
v
where
v
\mathbf v
v
is a
5
×
1
5\times1
5
×
1
matrix with real entries.
matrix
linear algebra