Given: linear transformation T: P₂ → P₂, T(a+bx+cr²) = (2a-b)+(a+b-3c)r+(c-a)r² a. Find the matrix representation A of T with respect to the ordered bases B = {1,2 + 1,2² +1} and B' = {1, 2, 2²}. b. Let g(x) = a + bx+cr² € P₂. Verify that A[q(r)]B = [T(q(x))]B'.
Given: linear transformation T: P₂ → P₂, T(a+bx+cr²) = (2a-b)+(a+b-3c)r+(c-a)r² a. Find the matrix representation A of T with respect to the ordered bases B = {1,2 + 1,2² +1} and B' = {1, 2, 2²}. b. Let g(x) = a + bx+cr² € P₂. Verify that A[q(r)]B = [T(q(x))]B'.
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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![Given: linear transformation T: P₂ → P2, T(a+bx+cr²) = (2a-b)+(a+b-3c)r+(c-a)r²
a. Find the matrix representation A of T with respect to the ordered bases B {1,2 +
1,2² +1} and B' = {1, 2, x²}.
b. Let g(x) = a +bx+cr² = P₂. Verify that A[q(r)]B = [T(g(x)) B¹.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41b4f204-8cf6-49b8-b430-685bf663cc88%2Fcf6648c0-96e4-42e2-8b33-f875fe7d78e2%2Fll9oipc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given: linear transformation T: P₂ → P2, T(a+bx+cr²) = (2a-b)+(a+b-3c)r+(c-a)r²
a. Find the matrix representation A of T with respect to the ordered bases B {1,2 +
1,2² +1} and B' = {1, 2, x²}.
b. Let g(x) = a +bx+cr² = P₂. Verify that A[q(r)]B = [T(g(x)) B¹.
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