2. Consider the linear transformation T: P2 (R) → M2x2 (R) defined byao + 2a2 ao - 3a₁4a0-12a₁ 2a0 + 402T(a₂x² + a₁x + ao) =Find the matrix for T, [T], whereB = {1, x, x²} C ={[%] [!] 8] 9]}200 10are bases for P2 (R) and M2x2 (R) respectively. Find bases for Ker(T) and Rng(T). Is Tone-to-one, onto, neither, or both?

Every linear transformation from a vector space to another vector space has a matrix representation…

2. Consider the linear transformation T: P₂ (R) → M2x2 (R) defined by ao + 2a2 T(a₂x² + a₁x + ao) = 4ao ao - 3a1 12a1 2ao + 4a2] Find the matrix for T, [T]g, where B = {1, x, x²} C = {[9.61.69.89]} are bases for P2(R) and M2x2 (R) respectively. Find bases for Ker(T) and Rng(T). Is T one-to-one, onto, neither, or both?

2. Consider the linear transformation T: P₂ (R) → M2x2 (R) defined by ao + 2a2 T(a₂x² + a₁x + ao) = 4ao ao - 3a1 12a1 2ao + 4a2] Find the matrix for T, [T]g, where B = {1, x, x²} C = {[9.61.69.89]} are bases for P2(R) and M2x2 (R) respectively. Find bases for Ker(T) and Rng(T). Is T one-to-one, onto, neither, or both?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.3: Matrices For Linear Transformations

Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.

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