The space P3 consists of all 3rd degree or less polynomials a + bx + cx² + dx³, and the standard basis for this space is the set {1, x, x², x³}. A polynomial such as 1 + 3x − 5x² + 4x³ would be represented 1 3 - 5 as Let N be the linear transformation from P3 to R³ defined by: N(p(x)) Answer: This is the transformation that evaluates the polynomial p(x) at x = 5 and x = 6, and evaluates its derivative at x = 6, and uses these values as the entries in a 3 x 1 vector. What should be the size of the matrix for this transformation? rows by = columns p(5) p(6) p'(6) b) Find the matrix T for this transformation with respect to the standard basis. Answer: T =
The space P3 consists of all 3rd degree or less polynomials a + bx + cx² + dx³, and the standard basis for this space is the set {1, x, x², x³}. A polynomial such as 1 + 3x − 5x² + 4x³ would be represented 1 3 - 5 as Let N be the linear transformation from P3 to R³ defined by: N(p(x)) Answer: This is the transformation that evaluates the polynomial p(x) at x = 5 and x = 6, and evaluates its derivative at x = 6, and uses these values as the entries in a 3 x 1 vector. What should be the size of the matrix for this transformation? rows by = columns p(5) p(6) p'(6) b) Find the matrix T for this transformation with respect to the standard basis. Answer: T =
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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Transcribed Image Text:The space P3 consists of all 3rd degree or less polynomials a + bx + cx² + dx³, and the standard basis
for this space is the set {1, x, x², x³}. A polynomial such as 1 + 3x − 5x² + 4x³ would be represented
1
3
- 5
as
Let N be the linear transformation from P3 to R³ defined by: N(p(x))
Answer:
This is the transformation that evaluates the polynomial p(x) at x = 5 and x = 6, and evaluates its
derivative at x = 6, and uses these values as the entries in a 3 x 1 vector.
What should be the size of the matrix for this transformation?
rows by
=
columns
p(5)
p(6)
p'(6)
b) Find the matrix T for this transformation with respect to the standard basis.
Answer: T =
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