8. (hint: see example 5 pg. 243) Consider the linear operator T: P3 → P3 given by T(p(x)) = 5p'(x) +p(x). a) Find the matrix representation for T relative to the standard basis B = = {1, x, x², x³}. b) Use this matrix to find 5p'(x) + p(x) for the polynomial p(x) = 5 + x - 3x² + x³. Show muoy Ho unde sans! I ([]) relative to basis B₁ = {e₁, e₂}. Then use Theorem 15 on page 250 to find 3 1 {[B].}]} [hint: see examples 2, 3 on page 251-252] 8 3 9. Find the matrix representation of the linear operator T: R2 → R2, given by T 2x Y x + 3y [T] B₂, where B₂ = = 10. Let V be the vector space of all polynomials (of any degree) and T: V → V the linear map T(p(x)) = p'(x). Explain why this mapping is not one to one. [9])
8. (hint: see example 5 pg. 243) Consider the linear operator T: P3 → P3 given by T(p(x)) = 5p'(x) +p(x). a) Find the matrix representation for T relative to the standard basis B = = {1, x, x², x³}. b) Use this matrix to find 5p'(x) + p(x) for the polynomial p(x) = 5 + x - 3x² + x³. Show muoy Ho unde sans! I ([]) relative to basis B₁ = {e₁, e₂}. Then use Theorem 15 on page 250 to find 3 1 {[B].}]} [hint: see examples 2, 3 on page 251-252] 8 3 9. Find the matrix representation of the linear operator T: R2 → R2, given by T 2x Y x + 3y [T] B₂, where B₂ = = 10. Let V be the vector space of all polynomials (of any degree) and T: V → V the linear map T(p(x)) = p'(x). Explain why this mapping is not one to one. [9])
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Help with question 9
![8. (hint: see example 5 pg. 243) Consider the linear operator T: P3 → P3 given by
T(p(x)) = 5p'(x) +p(x).
a) Find the matrix representation for T relative to the standard basis B =
= {1, x, x², x³}.
b) Use this matrix to find 5p'(x) + p(x) for the polynomial
p(x) = 5 + x - 3x² + x³.
Show muoy Ho unde sans! I
([])
relative to basis B₁ = {e₁, e₂}. Then use Theorem 15 on page 250 to find
3 1
{[B].}]}
[hint: see examples 2, 3 on page 251-252]
8
3
9. Find the matrix representation of the linear operator T: R2 → R2, given by T
2x Y
x + 3y
[T] B₂, where B₂ =
=
10. Let V be the vector space of all polynomials (of any degree) and T: V → V the linear
map T(p(x)) = p'(x). Explain why this mapping is not one to one.
[9])](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8783cbc5-0f10-43ba-8bd7-4625ee264f91%2F67933ed9-0b4c-4ac7-9652-62509a33c9e6%2Fv1btl2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8. (hint: see example 5 pg. 243) Consider the linear operator T: P3 → P3 given by
T(p(x)) = 5p'(x) +p(x).
a) Find the matrix representation for T relative to the standard basis B =
= {1, x, x², x³}.
b) Use this matrix to find 5p'(x) + p(x) for the polynomial
p(x) = 5 + x - 3x² + x³.
Show muoy Ho unde sans! I
([])
relative to basis B₁ = {e₁, e₂}. Then use Theorem 15 on page 250 to find
3 1
{[B].}]}
[hint: see examples 2, 3 on page 251-252]
8
3
9. Find the matrix representation of the linear operator T: R2 → R2, given by T
2x Y
x + 3y
[T] B₂, where B₂ =
=
10. Let V be the vector space of all polynomials (of any degree) and T: V → V the linear
map T(p(x)) = p'(x). Explain why this mapping is not one to one.
[9])
Expert Solution
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