Suppose T: P3-M2,2 is an isomorphism whose action is defined by 3a-3c -b-3c T(ax³ + bx²+cx+d)= -3c+d -b-3c+d and that we have the ordered bases B = 2 x3 " X " X, for P3 and M₂.2 respectively. a) Find the matrix of I corresponding to the ordered bases B and D. 000 MDB(T) =000 000 10 01 0 ¹ D= [] [83] [8] [9] 1 00 10 01 b) Find the matrix of I-1 corresponding to the ordered bases D and B. 0 0 0 MBD(T-¹) = 0 0 0 000 TIP: -0 q T-1 c) Describe the action of T-1 on a general matrix, using x as the variable for the polynomial and p, q, r, and s as constants. Use the '^' character to indicate an exponent, e.g. ax^2-bx+c.
Suppose T: P3-M2,2 is an isomorphism whose action is defined by 3a-3c -b-3c T(ax³ + bx²+cx+d)= -3c+d -b-3c+d and that we have the ordered bases B = 2 x3 " X " X, for P3 and M₂.2 respectively. a) Find the matrix of I corresponding to the ordered bases B and D. 000 MDB(T) =000 000 10 01 0 ¹ D= [] [83] [8] [9] 1 00 10 01 b) Find the matrix of I-1 corresponding to the ordered bases D and B. 0 0 0 MBD(T-¹) = 0 0 0 000 TIP: -0 q T-1 c) Describe the action of T-1 on a general matrix, using x as the variable for the polynomial and p, q, r, and s as constants. Use the '^' character to indicate an exponent, e.g. ax^2-bx+c.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Suppose T: P3→M2.2 is an isomorphism whose action is defined by
3a-3c -b-3c
T(ax³ + bx²+cx+d)=
-3c+d -b-3c+d
and that we have the ordered bases
=√x³, x²,
3
B =
for P3 and M2,2 respectively.
a) Find the matrix of I corresponding to the ordered bases B and D.
000
MDB(T) 0 0 0
000
MBD(T-1):
X ,
=
b) Find the matrix of T-1 corresponding to the ordered bases D and B.
T-1
p q
-0
01
1 D=
¹ D- [10] - [ 1 ] - [ ] [ ]
"
00 00
01
c) Describe the action of I-1 on a general matrix, using x as the variable for the polynomial and p, q, r, and s as constants.
Use the '^' character to indicate an exponent, e.g. ax^2-bx+c.
r s
000
000
000](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F373110e7-e385-4127-adf5-b0ae0e197db9%2F1fd7fb8c-b726-49ff-8ca3-fb4c6efaa179%2Fm6p1cdd_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose T: P3→M2.2 is an isomorphism whose action is defined by
3a-3c -b-3c
T(ax³ + bx²+cx+d)=
-3c+d -b-3c+d
and that we have the ordered bases
=√x³, x²,
3
B =
for P3 and M2,2 respectively.
a) Find the matrix of I corresponding to the ordered bases B and D.
000
MDB(T) 0 0 0
000
MBD(T-1):
X ,
=
b) Find the matrix of T-1 corresponding to the ordered bases D and B.
T-1
p q
-0
01
1 D=
¹ D- [10] - [ 1 ] - [ ] [ ]
"
00 00
01
c) Describe the action of I-1 on a general matrix, using x as the variable for the polynomial and p, q, r, and s as constants.
Use the '^' character to indicate an exponent, e.g. ax^2-bx+c.
r s
000
000
000
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