Let T : V β V be a linear transformation, where B = { v 1 , v 2 , v 3 , v 4 } is a basis for V . Find the matrix representation of T with respect to B if T ( v 1 ) = v 2 , T ( v 2 ) = v 3 , T ( v 3 ) = v 1 + v 2 , and T ( v 4 ) = v 1 + 3 v 4 .
Let T : V β V be a linear transformation, where B = { v 1 , v 2 , v 3 , v 4 } is a basis for V . Find the matrix representation of T with respect to B if T ( v 1 ) = v 2 , T ( v 2 ) = v 3 , T ( v 3 ) = v 1 + v 2 , and T ( v 4 ) = v 1 + 3 v 4 .
Solution Summary: The author explains that the matrix representation of T is given as, left[cc
Let
T
:
V
→
V
be a linear transformation, where
B
=
{
v
1
,
v
2
,
v
3
,
v
4
}
is a basis for
V
. Find the matrix representation of
T
with respect to
B
if
T
(
v
1
)
=
v
2
,
T
(
v
2
)
=
v
3
,
T
(
v
3
)
=
v
1
+
v
2
, and
T
(
v
4
)
=
v
1
+
3
v
4
.
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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