Let T : P;(R) → PĄ(R) be a linear transformation. If the matrix representation of T in the standard bases 3 = {1, x, x², x³, xª, x³} and y = {1, x, x², x³, xª} is 0 1 0 0 0 0 0 0 2 0 0 0 A= |0 0 0 3 0 0 0 0 0 0 4 0 0 0 0 0 0 5 then, using the change of coordinate matrix formula, find the matrix representation of T in the ordered bases: B' = {1, 1+x, 1+x+x², 1+x+x² +x*, 1+x+x² + r³ + x*, 1+x +x² +x³ + x* + x° } and y = {1, 2x, 3x², 4x³, 5xª}.

Let T : P;(R) → PĄ(R) be a linear transformation. If the matrix representation of T in the standard bases 3 = {1, x, x², x³, xª, x³} and y = {1, x, x², x³, xª} is 0 1 0 0 0 0 0 0 2 0 0 0 A= |0 0 0 3 0 0 0 0 0 0 4 0 0 0 0 0 0 5 then, using the change of coordinate matrix formula, find the matrix representation of T in the ordered bases: B' = {1, 1+x, 1+x+x², 1+x+x² +x, 1+x+x² + r³ + x, 1+x +x² +x³ + x* + x° } and y = {1, 2x, 3x², 4x³, 5xª}.

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

Let T : P;(R) → PĄ(R) be a linear transformation. If the matrix representation of T
in the standard bases 3 = {1, x, x², x³, xª, x³} and y = {1, x, x², x³, xª} is
0 1 0 0 0 0
0 0 20 0 0
A = |0 0 0 30 0
0 0 0 0 4 0
0 0 0 0 05
then, using the change of coordinate matrix formula, find the matrix representation of T
in the ordered bases:
B' = {1, 1+x, 1+x+x², 1+x +x² +x³, 1+x + x² + x³ + x*, 1+x +x² + x³ +x* + x° }
and y = {1, 2x, 3x², 4x³, 5x4}.

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