A linear operator T: P2 P2 is defined as T(p(x)) = p(2x+1), i.e. T(c + c₁x + c₂x²) = C₁ + c₁ (2x + 1) + c₁ (2x + 1)² a. Find a matrix [T]Å where B is the basis B = {1, x, x²} b. Perform the 3-step procedure to find T(2 − 3x + 4x²) c. Compare the result obtained in b, with the result of T(2 − 3x + 4x²) obtained directly
A linear operator T: P2 P2 is defined as T(p(x)) = p(2x+1), i.e. T(c + c₁x + c₂x²) = C₁ + c₁ (2x + 1) + c₁ (2x + 1)² a. Find a matrix [T]Å where B is the basis B = {1, x, x²} b. Perform the 3-step procedure to find T(2 − 3x + 4x²) c. Compare the result obtained in b, with the result of T(2 − 3x + 4x²) obtained directly
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 18CM
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![2. A linear operator T: P₂ P2 is defined as
T(p(x)) = p(2x+1), i.e. T(c + C₁x + C₂x²) = C₁ + c₁ (2x + 1) + c₁ (2x + 1)²
a. Find a matrix [T] B where B is the basis B = {1, x, x²}
b. Perform the 3-step procedure to find T(2 − 3x + 4x²)
c. Compare the result obtained in b, with the result of T(2 − 3x + 4x²) obtained directly](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F780135a8-f701-479c-be02-38c3a3de7347%2F2bd3d618-b564-4a64-92ca-3768965c49cb%2Ft665rlz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. A linear operator T: P₂ P2 is defined as
T(p(x)) = p(2x+1), i.e. T(c + C₁x + C₂x²) = C₁ + c₁ (2x + 1) + c₁ (2x + 1)²
a. Find a matrix [T] B where B is the basis B = {1, x, x²}
b. Perform the 3-step procedure to find T(2 − 3x + 4x²)
c. Compare the result obtained in b, with the result of T(2 − 3x + 4x²) obtained directly
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