Let S be the transformation in Exercise 14 , let the basis for P 2 be B = { 1 , x , x 2 } , and let the basis for P 3 be D = { 3 , 3 x − x 2 , 3 x 2 , x 3 } . Find the matrix for S . Let S : P 2 → P 3 be given by S ( P ) = x 3 p ″ − x 2 p ′ + 3 p . Find the matrix representation of S with respect to the natural bases B = { 1 , x , x 2 } for P 2 and C = { 1 , x , x 2 , x 3 } for P 3 .
Let S be the transformation in Exercise 14 , let the basis for P 2 be B = { 1 , x , x 2 } , and let the basis for P 3 be D = { 3 , 3 x − x 2 , 3 x 2 , x 3 } . Find the matrix for S . Let S : P 2 → P 3 be given by S ( P ) = x 3 p ″ − x 2 p ′ + 3 p . Find the matrix representation of S with respect to the natural bases B = { 1 , x , x 2 } for P 2 and C = { 1 , x , x 2 , x 3 } for P 3 .
Solution Summary: The author explains how the matrix representation of S is given as, left[cc1& 0&
Let
S
be the transformation in Exercise
14
, let the basis for
P
2
be
B
=
{
1
,
x
,
x
2
}
, and let the basis for
P
3
be
D
=
{
3
,
3
x
−
x
2
,
3
x
2
,
x
3
}
. Find the matrix for
S
. Let
S
:
P
2
→
P
3
be given by
S
(
P
)
=
x
3
p
″
−
x
2
p
′
+
3
p
. Find the matrix representation of
S
with respect to the natural bases
B
=
{
1
,
x
,
x
2
}
for
P
2
and
C
=
{
1
,
x
,
x
2
,
x
3
}
for
P
3
.
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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