Let T: P₂ → P₁ be the linear transformation defined by T(αo + a₁x + a₂x²) = (ao + a₁) − (2 a₁ + 3a₂)x. i. Find the matrix T relative to the standard bases B = {1, x, x²} and B' = {1, x} for P₂ and P₁. ii. Verify that the matrix [T] B¹, B obtained in part (i) satisfies formula for every vector x = co + C₁x + c₂x² in P₂.
Let T: P₂ → P₁ be the linear transformation defined by T(αo + a₁x + a₂x²) = (ao + a₁) − (2 a₁ + 3a₂)x. i. Find the matrix T relative to the standard bases B = {1, x, x²} and B' = {1, x} for P₂ and P₁. ii. Verify that the matrix [T] B¹, B obtained in part (i) satisfies formula for every vector x = co + C₁x + c₂x² in P₂.
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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![Let T: P₂ → P₁ be the linear transformation defined by
T(αo + a₁x + a₂x²) = (ao + a₁) − (2 a₁ + 3a₂)x.
i. Find the matrix T relative to the standard bases B = {1, x, x²} and B' = {1, x} for P₂ and
P₁.
ii. Verify that the matrix [T] B¹, B obtained in part (i) satisfies formula
for every vector x = co + C₁x + c₂x² in P₂.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F498ceea7-61aa-4cb3-8641-56e69c93be55%2Feb4cb696-99a9-4e70-92a9-19fc4434a69a%2Fbzrssmk_processed.png&w=3840&q=75)
Transcribed Image Text:Let T: P₂ → P₁ be the linear transformation defined by
T(αo + a₁x + a₂x²) = (ao + a₁) − (2 a₁ + 3a₂)x.
i. Find the matrix T relative to the standard bases B = {1, x, x²} and B' = {1, x} for P₂ and
P₁.
ii. Verify that the matrix [T] B¹, B obtained in part (i) satisfies formula
for every vector x = co + C₁x + c₂x² in P₂.
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