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Vector Spaces · 2.4.6
Physics
Problem
Suppose
A
A
A
is an
m
m
m
by
n
n
n
matrix of rank
r
r
r
. Under what conditions on those numbers does (a)
A
A
A
have a two-sided inverse:
A
A
−
1
=
A
−
1
A
=
I
AA^{-1} = A^{-1}A = I
A
A
−
1
=
A
−
1
A
=
I
? (b)
A
x
=
b
Ax = b
A
x
=
b
have infinitely many solutions for every
b
b
b
?
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