Let T be the linear transformation defined in Exercise 21 . If Q is the matrix representation found in Exercise 21 , show that Q [ p ] B = [ T ( p ) ] B for p ( x ) = a 0 + a 1 x + a 2 x 2 . Let T : P 2 → P 2 be defined by T ( a 0 + a 1 x + a 3 x 2 ) = ( − 4 a 0 − 2 a 1 ) + ( 3 a 0 + 3 a 1 ) x + ( − a 0 + 2 a 1 + 3 a 2 ) x 2 . Determine the matrix of T relative to the natural basis B for P 2 .
Let T be the linear transformation defined in Exercise 21 . If Q is the matrix representation found in Exercise 21 , show that Q [ p ] B = [ T ( p ) ] B for p ( x ) = a 0 + a 1 x + a 2 x 2 . Let T : P 2 → P 2 be defined by T ( a 0 + a 1 x + a 3 x 2 ) = ( − 4 a 0 − 2 a 1 ) + ( 3 a 0 + 3 a 1 ) x + ( − a 0 + 2 a 1 + 3 a 2 ) x 2 . Determine the matrix of T relative to the natural basis B for P 2 .
Solution Summary: The author explains how the expression Qleft[pright]_B = 'left' for the matrix representation T:Uto V is verified as given below.
Let
T
be the linear transformation defined in Exercise
21
. If
Q
is the matrix representation found in Exercise
21
, show that
Q
[
p
]
B
=
[
T
(
p
)
]
B
for
p
(
x
)
=
a
0
+
a
1
x
+
a
2
x
2
.
Let
T
:
P
2
→
P
2
be defined by
T
(
a
0
+
a
1
x
+
a
3
x
2
)
=
(
−
4
a
0
−
2
a
1
)
+
(
3
a
0
+
3
a
1
)
x
+
(
−
a
0
+
2
a
1
+
3
a
2
)
x
2
. Determine the matrix of
T
relative to the natural basis
B
for
P
2
.
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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