P3 = {ao + a¡t + azt² + a3t³ : ao, a1, az E R}be the vector space consisting of all polynomials of degree less than or equal to 3. Observbasis for P3, whereB = {1, t, t², t³}.Let T : P3- P3 be a linear transformation defined byT(ao + ajt + azt² + a3t°) = a1 + 2a2 + 6aztFind the matrix representation [T]B_of T with respect to B.

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P3 = {ao + a¡t + a2t² + azt: ao, a1, a3 E R} be the vector space consisting of all polynomials of degree less than or equal to 3. Observ basis for P3, where B = {1, 1, t², t³ }. Let T : P3 → P3 be a linear transformation defined by T(ao + a¡t + azt² + azt³) = aj + 2a2 + 6azt Find the matrix representation [T]B_of T with respect to B.

P3 = {ao + a¡t + a2t² + azt: ao, a1, a3 E R} be the vector space consisting of all polynomials of degree less than or equal to 3. Observ basis for P3, where B = {1, 1, t², t³ }. Let T : P3 → P3 be a linear transformation defined by T(ao + a¡t + azt² + azt³) = aj + 2a2 + 6azt Find the matrix representation [T]B_of T with respect to B.

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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Question

P3 = {ao + a¡t + azt² + a3t³ : ao, a1, az E R}
be the vector space consisting of all polynomials of degree less than or equal to 3. Observ
basis for P3, where
B = {1, t, t², t³}.
Let T : P3
- P3 be a linear transformation defined by
T(ao + ajt + azt² + a3t°) = a1 + 2a2 + 6azt
Find the matrix representation [T]B_of T with respect to B.

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