2. Consider the linear transformation T : P2(IR) → M2x2(R) defined byao + 2a24aо — 12ал 2ао + 4a2За1T(a2x2 + a1x + ao)Find the matrix for T, [T, where[o 1][o o][o o]B = {1, x, x²} C=are bases for P2(R) and M2x2(IR) respectively. Find bases for Ker(T) and Rng(T). Is Tone-to-one, onto, neither, or both?

1st we find the matrix for T by using the bases. Then find the Ker(T) and Rng(T). After that from…

2. Consider the linear transformation T : P2(R) → M2×2(R) defined by За1 ao + 2a2 |4ао — 12а, 2аg + 4a2 ao T(a2x? + a1x + ao) Find the matrix for T, [T], where 0] [o B = {1, x, x²} C = 0 are bases for P(R) and M2x2(R) respectively. Find bases for Ker(T) and Rng(T). Is 7 one-to-one, onto, neither, or both?

2. Consider the linear transformation T : P2(R) → M2×2(R) defined by За1 ao + 2a2 |4ао — 12а, 2аg + 4a2 ao T(a2x? + a1x + ao) Find the matrix for T, [T], where 0] [o B = {1, x, x²} C = 0 are bases for P(R) and M2x2(R) respectively. Find bases for Ker(T) and Rng(T). Is 7 one-to-one, onto, neither, or both?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 23EQ

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