Let { v 1 , v 2 } be a basis for the vector space V , and suppose that T : V → V is a linear transformation. If T ( v 1 ) = v 1 + 2 v 2 and T ( v 2 ) = 2 v 1 − 3 v 2 , determine whether T is one-to-one, onto, both, or neither. Find T − 1 or explain why it does not exist.
Let { v 1 , v 2 } be a basis for the vector space V , and suppose that T : V → V is a linear transformation. If T ( v 1 ) = v 1 + 2 v 2 and T ( v 2 ) = 2 v 1 − 3 v 2 , determine whether T is one-to-one, onto, both, or neither. Find T − 1 or explain why it does not exist.
Solution Summary: The author explains how to determine whether the transformation T is one-to-one, onto, both, or neither.
Let
{
v
1
,
v
2
}
be a basis for the vector space
V
, and suppose that
T
:
V
→
V
is a linear transformation. If
T
(
v
1
)
=
v
1
+
2
v
2
and
T
(
v
2
)
=
2
v
1
−
3
v
2
, determine whether
T
is one-to-one, onto, both, or neither. Find
T
−
1
or explain why it does not exist.
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