6. Let T: P₂ → P₂ be the linear operator defined as T (p(x)) = p(3x), and let B = {1, x,x²} be the standard basis for P₂. Find [T], the matrix for T relative to B. ) Let p(x) = 1 -x + 4x². Determine [p(x)]g, then find T(p(x)) using [7] from part a. Check your answer to part b by evaluating T(1-x + 4x²) directly.
6. Let T: P₂ → P₂ be the linear operator defined as T (p(x)) = p(3x), and let B = {1, x,x²} be the standard basis for P₂. Find [T], the matrix for T relative to B. ) Let p(x) = 1 -x + 4x². Determine [p(x)]g, then find T(p(x)) using [7] from part a. Check your answer to part b by evaluating T(1-x + 4x²) directly.
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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![6. Let T: P₂ → P₂ be the linear operator defined as T (p(x)) = p(3x), and let B = {1, x, x²} be the standard
basis for P₂.
Find [7], the matrix for T relative to B.
) Let p(x) = 1 -x + 4x². Determine [p(x)]B, then find T (p(x)) using [T]g from part a.
Check your answer to part b by evaluating T(1-x + 4x²) directly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed7b56a3-2e66-4877-848b-86d54658cb11%2F29b893d6-5c51-4e7b-92f8-83fbc8b46282%2F8lho7wq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Let T: P₂ → P₂ be the linear operator defined as T (p(x)) = p(3x), and let B = {1, x, x²} be the standard
basis for P₂.
Find [7], the matrix for T relative to B.
) Let p(x) = 1 -x + 4x². Determine [p(x)]B, then find T (p(x)) using [T]g from part a.
Check your answer to part b by evaluating T(1-x + 4x²) directly.
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