Find [T], [T]G, and [T]. 8. Consider the following basis for R²: *-(8-8) {[ 3 Let T: R² R² be a linear transformation defined by T(v) = Av, where A is the matrix B = is a basis of R³. 2 3 5 -1 Find [T]B. 9. Let T be the linear transformation T: P3 → R³ defined by ]. 3a + d -2c + b a+c Find [T], where E = {1, x, x², x³} is the standard basis of P3 and B = T(a+bx+cx² + dx³) = 1 0 --{8-8-8) 0 0
Find [T], [T]G, and [T]. 8. Consider the following basis for R²: *-(8-8) {[ 3 Let T: R² R² be a linear transformation defined by T(v) = Av, where A is the matrix B = is a basis of R³. 2 3 5 -1 Find [T]B. 9. Let T be the linear transformation T: P3 → R³ defined by ]. 3a + d -2c + b a+c Find [T], where E = {1, x, x², x³} is the standard basis of P3 and B = T(a+bx+cx² + dx³) = 1 0 --{8-8-8) 0 0
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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Q9 solution needed
![Find [T], [T]G, and [T].
8. Consider the following basis for R²:
1
2
B = {[ 3 ] - [ 3 ]}
4
Let T : R² → R² be a linear transformation defined by T(v) = Av, where A is the matrix
Find [T]B.
9. Let T be the linear transformation T : P3 → R³ defined by
is a basis of R³.
2
[33]
5
T(a+bx+cx² + dx³)
B
=
B
Find [T], where E = {1, x, x², x³} is the standard basis of P3 and
E
=
3a + d
-2c + b
a + c
1
0
-{8.84]}
0
0
1.
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7eb27733-b5b9-4f80-b991-53bace93f5ba%2F25490fe1-bcb1-47f8-9a9b-6f20df9a2c8e%2Fwpl8qf_processed.png&w=3840&q=75)
Transcribed Image Text:Find [T], [T]G, and [T].
8. Consider the following basis for R²:
1
2
B = {[ 3 ] - [ 3 ]}
4
Let T : R² → R² be a linear transformation defined by T(v) = Av, where A is the matrix
Find [T]B.
9. Let T be the linear transformation T : P3 → R³ defined by
is a basis of R³.
2
[33]
5
T(a+bx+cx² + dx³)
B
=
B
Find [T], where E = {1, x, x², x³} is the standard basis of P3 and
E
=
3a + d
-2c + b
a + c
1
0
-{8.84]}
0
0
1.
1
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