3. Let B₁ = {1,2, x²} and B₂ = {x − 1, 2² - x - 1,1} be two bases of P2 (R). Let C₁ = {1, 2, €3} and C₂ = {e1 - e2, 3, €1 + 2 + 3} be two bases of R³. Suppose that T: P₂ (R) → R³ is a linear transformation such that, with respect to bases B₁ and C₁, the matrix of T is given by [111] M(T) = 1 1 0 [201 Find the matrix of T with respect to the bases B₂ and C₂.

3. Let B₁ = {1,2, x²} and B₂ = {x − 1, 2² - x - 1,1} be two bases of P2 (R). Let C₁ = {1, 2, €3} and C₂ = {e1 - e2, 3, €1 + 2 + 3} be two bases of R³. Suppose that T: P₂ (R) → R³ is a linear transformation such that, with respect to bases B₁ and C₁, the matrix of T is given by [111] M(T) = 1 1 0 [201 Find the matrix of T with respect to the bases B₂ and C₂.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 3EQ: In Exercises 1-12, determine whether T is a linear transformation. T:MnnMnn defines by T(A)=AB,...

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