2. Consider the linear transformation T: P2 → R³ defined by T(ax+b+c)= ( a+b b+c c+a (a) Compute M = [T]Bw where By = {1, x, x2} and Bw is the standard basis for R³. (b) Compute M-1 by hand using the augmented matrix approach and elementary row opertions. (c) Use Mto determine T-¹.

2. Consider the linear transformation T: P2 → R³ defined by T(ax+b+c)= ( a+b b+c c+a (a) Compute M = [T]Bw where By = {1, x, x2} and Bw is the standard basis for R³. (b) Compute M-1 by hand using the augmented matrix approach and elementary row opertions. (c) Use Mto determine T-¹.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 8E

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Question

2. Consider the linear transformation T: P2 → R³ defined by
T(ax+b+c)=
(
a+b
b+c
c+a
(a) Compute M = [T]Bw where By = {1, x, x2} and Bw is the standard basis for R³.
(b) Compute M-1 by hand using the augmented matrix approach and elementary row opertions.
(c) Use Mto determine T-¹.

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