B = (1. x + 1,x² + x) forms an ordered basis for P3. Give the B-coordinate vector of each of File Preview ing vectors. That is, for each of the following p determine what is [p]. VII (a) 2+3x+4x² (b) 5+7x+3x² (c) 1 + x (d) 2 + x Let 3 be the ordered basis for P3 from the previous problem and T: P3 → P3 be given by p(x). Find a matrix A € R³×³ so that [T(p)] = A[p] T(p) = = for all polynomials p € P3.
B = (1. x + 1,x² + x) forms an ordered basis for P3. Give the B-coordinate vector of each of File Preview ing vectors. That is, for each of the following p determine what is [p]. VII (a) 2+3x+4x² (b) 5+7x+3x² (c) 1 + x (d) 2 + x Let 3 be the ordered basis for P3 from the previous problem and T: P3 → P3 be given by p(x). Find a matrix A € R³×³ so that [T(p)] = A[p] T(p) = = for all polynomials p € P3.
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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Please answer the question after the question with parts a-d using the question with parts a-d.
![B = (1. x + 1,x² + x) forms an ordered basis for P3. Give the B-coordinate vector of each of
ving vectors. That is, for each of the following p determine what is [p].
File Preview
(a) 2+3x+4x²
(b) 5+7x+3x²
(c) 1 + x
(d) 2 + x
Let 3 be the ordered basis for P3 from the previous problem and T : P3 → P3 be given by
T(p) = p(x). Find a matrix A € R³×³ so that
[T(p)] = A[p]B
for all polynomials p € P3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4217e83c-b4b2-47da-9d7a-2d6031448fca%2F8b9037ab-9e2a-40c5-8de6-fb16ed8af166%2Fi9uvgba_processed.png&w=3840&q=75)
Transcribed Image Text:B = (1. x + 1,x² + x) forms an ordered basis for P3. Give the B-coordinate vector of each of
ving vectors. That is, for each of the following p determine what is [p].
File Preview
(a) 2+3x+4x²
(b) 5+7x+3x²
(c) 1 + x
(d) 2 + x
Let 3 be the ordered basis for P3 from the previous problem and T : P3 → P3 be given by
T(p) = p(x). Find a matrix A € R³×³ so that
[T(p)] = A[p]B
for all polynomials p € P3.
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