The linear tranformation L defined by L(p(x)) = -7p' + 8p" maps P4 into P3. (a) Find the matrix representation of L with respect to the ordered bases S= E = {x³, x², x, 1} and F = {x² + x + 1, x + 1, 1} (b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = -8x³ 11x and g(x) = x² - 13. [L(p(x))]F: [L(g(x))] F =
The linear tranformation L defined by L(p(x)) = -7p' + 8p" maps P4 into P3. (a) Find the matrix representation of L with respect to the ordered bases S= E = {x³, x², x, 1} and F = {x² + x + 1, x + 1, 1} (b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = -8x³ 11x and g(x) = x² - 13. [L(p(x))]F: [L(g(x))] F =
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 55EQ
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![The linear tranformation L defined by
L(p(x)) = -7p' + 8p"
maps P4 into P3.
(a) Find the matrix representation of L with respect to the ordered bases
S=
E = {x³, x², x, 1} and F = {x² + x + 1, x + 1, 1}
(b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = -8x³ - 11x and g(x) = x² - 13.
[L(p(x))]F:
[L(g(x))] F =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fe0f2e6-a3fe-44ed-a932-d5c5d1248f5a%2Fa1c1de0e-75ce-4b2f-bff4-a423278bdfa1%2Fqqqzblq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The linear tranformation L defined by
L(p(x)) = -7p' + 8p"
maps P4 into P3.
(a) Find the matrix representation of L with respect to the ordered bases
S=
E = {x³, x², x, 1} and F = {x² + x + 1, x + 1, 1}
(b) Use Part (a) to find the coordinate vectors of L(p(x)) and L(g(x)) where p(x) = -8x³ - 11x and g(x) = x² - 13.
[L(p(x))]F:
[L(g(x))] F =
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