2. Let P2(C) be a vector space of polynomials of degree less than or equal to 2over R.(a) By using linear extension method, show that P2(C) is isomorphic toC3.(b) Let T : P2(C) → C³ be a transformation such thatT(a + bx + cx²) = (a,a+ b,a + b+ c).Find the matrix representation T relative to the standard basis.

Answered: Image /qna-images/answer/ba402de0-96f5-4c11-beaf-69139fb4f677.jpg

2. Let P2(C) be a vector space of polynomials of degree less than or equal to 2 over R. (a) By using linear extension method, show that P2(C) is isomorphic to C³. (b) Let T : P2(C) +C³ be a transformation such that T(a + bx + cr²) = (a,a+ b,a+ b+c). Find the matrix representation T relative to the standard basis.

2. Let P2(C) be a vector space of polynomials of degree less than or equal to 2 over R. (a) By using linear extension method, show that P2(C) is isomorphic to C³. (b) Let T : P2(C) +C³ be a transformation such that T(a + bx + cr²) = (a,a+ b,a+ b+c). Find the matrix representation T relative to the standard basis.

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,...

See similar textbooks