Let T be a linear transformation from P2 into P2 such that T(1) = x, T(x) = 1 + x, and T(x2) = 1 + x + x2. Find T(1 − 7x + 2x2). T(1 − 7x + 2x2)

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Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.CR: Review Exercises

Problem 20CR: Let T be a linear transformation from R3 into R such that T(1,1,1)=1, T(1,1,0)=2 and T(1,0,0)=3....

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Question

Let T be a linear transformation from P₂ into P₂ such that

T(1) = x, T(x) = 1 + x, and T(x²) = 1 + x + x².

Find

T(1 − 7x + 2x²).

T(1 − 7x + 2x²)

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