Let T: P2 that is, 7. > P2 be the linear operator T(p(x)) = p(2x+ 1), T(co+ C,x+ C,x²) = c, + c,(2x + 1) + c,(2x + 1)? a. Find [T]B with respect to the basis B = {1,x, x?}. b. Use the three-step procedure illustrated in Example 2 to compute T(2 – 3x + 4x²). c. Check the result obtained in part (b) by computing T(2 3x+ 4x2) directly.
Let T: P2 that is, 7. > P2 be the linear operator T(p(x)) = p(2x+ 1), T(co+ C,x+ C,x²) = c, + c,(2x + 1) + c,(2x + 1)? a. Find [T]B with respect to the basis B = {1,x, x?}. b. Use the three-step procedure illustrated in Example 2 to compute T(2 – 3x + 4x²). c. Check the result obtained in part (b) by computing T(2 3x+ 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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![7.
Let T: P2
> P2 be the linear operator T(p(x)) = p(2x + 1),
that is,
T(co + c,x+ C,x²) = co + c,(2x + 1) + c,(2x + 1)²
a. Find [T]B with respect to the basis B =
{1,x, x?}.
b. Use the three-step procedure illustrated in Example 2 to
compute T(2 – 3x + 4x²).
c. Check the result obtained in part (b) by computing
T(2 3x + 4x²) directly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05419715-1bd0-4457-a143-03af22167dbf%2Ff53333c9-4eb8-47e5-90f8-f21e4c741e17%2Fx6bqrks_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7.
Let T: P2
> P2 be the linear operator T(p(x)) = p(2x + 1),
that is,
T(co + c,x+ C,x²) = co + c,(2x + 1) + c,(2x + 1)²
a. Find [T]B with respect to the basis B =
{1,x, x?}.
b. Use the three-step procedure illustrated in Example 2 to
compute T(2 – 3x + 4x²).
c. Check the result obtained in part (b) by computing
T(2 3x + 4x²) directly.
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