Let T : R n → R m be a linear transformation with nullity zero. If S = { x 1 , ⋯ , x k } is a linearly independent subset of R n , then show that { T ( x 1 ) , ⋯ , T ( x k ) } is a linearly independent subset of R m .
Let T : R n → R m be a linear transformation with nullity zero. If S = { x 1 , ⋯ , x k } is a linearly independent subset of R n , then show that { T ( x 1 ) , ⋯ , T ( x k ) } is a linearly independent subset of R m .
Solution Summary: The author explains that T:Rnto rm is a linear transformation with nullity zero. It satisfies the following properties:
Let
T
:
R
n
→
R
m
be a linear transformation with nullity zero. If
S
=
{
x
1
,
⋯
,
x
k
}
is a linearly independent subset of
R
n
, then show that
{
T
(
x
1
)
,
⋯
,
T
(
x
k
)
}
is a linearly independent subset of
R
m
.
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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