Let T be the linear transformation defined in Exercise 21 . Find the matrix of T with respect to the basis C = { 1 − 3 x + 7 x 2 , 6 − 3 x + 2 x 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 . Find the matrix of T with respect to the basis C = { 1 − 3 x + 7 x 2 , 6 − 3 x + 2 x 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 the matrix representation of T with respect to the given basis for P_2.
Let
T
be the linear transformation defined in Exercise
21
. Find the matrix of
T
with respect to the basis
C
=
{
1
−
3
x
+
7
x
2
,
6
−
3
x
+
2
x
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
.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
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