Let T : R n β R n be a linear transformation, and suppose that S = { x 1 , ... , x k } is a subset of R n such that { T ( x 1 ) , ... , T ( x k ) } is a linearly independent subset of R m . Show that the set S is linearly independent.
Let T : R n β R n be a linear transformation, and suppose that S = { x 1 , ... , x k } is a subset of R n such that { T ( x 1 ) , ... , T ( x k ) } is a linearly independent subset of R m . Show that the set S is linearly independent.
Solution Summary: The author explains how S=leftx_1,mathrm... is a linearly independent subset of Rn.
Let
T
:
R
n
→
R
n
be a linear transformation, and suppose that
S
=
{
x
1
,
...
,
x
k
}
is a subset of
R
n
such that
{
T
(
x
1
)
,
...
,
T
(
x
k
)
}
is a linearly independent subset of
R
m
. Show that the set
S
is linearly independent.
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Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY