. Let B = [X³, X², X, 1] and C = [1, X, X²], which are ordered bases for P3(R) and P2 (R), respectively. (Note the orders of these bases!) Define T: P3(R) → P₂(R) by T(f) = f'. (a) Compute c[T] B. (b) Let f(X) = 4-5X²+2X³. Compute B[f]. Compute T(f). (c) Define S: P₂ (R) → R² by S(f) = (f(-1), f(1)). Compute D[S]c, where D is the standard ordered basis of R². Compute D[ST]B, the matrix of the composition ST with respect to the bases B and D.
. Let B = [X³, X², X, 1] and C = [1, X, X²], which are ordered bases for P3(R) and P2 (R), respectively. (Note the orders of these bases!) Define T: P3(R) → P₂(R) by T(f) = f'. (a) Compute c[T] B. (b) Let f(X) = 4-5X²+2X³. Compute B[f]. Compute T(f). (c) Define S: P₂ (R) → R² by S(f) = (f(-1), f(1)). Compute D[S]c, where D is the standard ordered basis of R². Compute D[ST]B, the matrix of the composition ST with respect to the bases B and D.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![11. Let B = [X³, X², X, 1] and C
=
[1, X, X²], which are ordered bases for P3(R) and
P₂ (R), respectively. (Note the orders of these bases!) Define T: P3(R) → P₂ (R) by
T(f) = f'.
(a) Compute c[T]B.
(b) Let f(X) = 4-5X²+2X³. Compute B[f]. Compute T(f).
(c) Define S: P₂ (R) → R² by S(f) = (f(-1), f(1)). Compute D[S]c, where D is the
standard ordered basis of R2. Compute D[ST]3, the matrix of the composition
ST with respect to the bases B and D.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45e9ceaf-0062-410b-addf-404f0a3b8197%2F652f56e8-bccd-429c-8a9c-b7e2cfe25fe0%2F2dcf4ut_processed.png&w=3840&q=75)
Transcribed Image Text:11. Let B = [X³, X², X, 1] and C
=
[1, X, X²], which are ordered bases for P3(R) and
P₂ (R), respectively. (Note the orders of these bases!) Define T: P3(R) → P₂ (R) by
T(f) = f'.
(a) Compute c[T]B.
(b) Let f(X) = 4-5X²+2X³. Compute B[f]. Compute T(f).
(c) Define S: P₂ (R) → R² by S(f) = (f(-1), f(1)). Compute D[S]c, where D is the
standard ordered basis of R2. Compute D[ST]3, the matrix of the composition
ST with respect to the bases B and D.
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