A linear transformation L : V → W is said to be one−to−one if L ( v 1 ) = L ( v 2 ) implies that v 1 = v 2 (i.e., no two distinct vectors v 1 , v 2 in V get mapped into the same vector w ∈ W ). Show that L is one−to−one if and only if ker ( L ) = { 0 v } .
A linear transformation L : V → W is said to be one−to−one if L ( v 1 ) = L ( v 2 ) implies that v 1 = v 2 (i.e., no two distinct vectors v 1 , v 2 in V get mapped into the same vector w ∈ W ). Show that L is one−to−one if and only if ker ( L ) = { 0 v } .
Solution Summary: The author explains that a linear transformation L:Vto W is said to be one-to-one if v_1)=L(
A linear transformation
L
:
V
→
W
is said to be one−to−one if
L
(
v
1
)
=
L
(
v
2
)
implies that
v
1
=
v
2
(i.e., no two distinct vectors
v
1
,
v
2
in V get mapped into the same vector
w
∈
W
). Show that L is one−to−one if and only if
ker
(
L
)
=
{
0
v
}
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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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