Let A be an m × n matrix of rank r and let { x 1 , . . . , x r } be a basis for R ( A T ) . Show that { A x 1 , . . . , A x r } is a basis for R ( A ) .
Let A be an m × n matrix of rank r and let { x 1 , . . . , x r } be a basis for R ( A T ) . Show that { A x 1 , . . . , A x r } is a basis for R ( A ) .
Solution Summary: The author explains that leftAx_1,mathrm.... and yin R ( AT) are basis
Let A be an
m
×
n
matrix of rank r and let
{
x
1
,
.
.
.
,
x
r
}
be a basis for
R
(
A
T
)
.
Show that
{
A
x
1
,
.
.
.
,
A
x
r
}
is a basis for
R
(
A
)
.
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