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(а+ bx + сa?) — (а, а + b, а +ь+ c).=Find the matrix representation T relative to the standard basis.

Answered: Image /qna-images/answer/8dcec5f2-4aa2-4c7f-b282-dc71afffb290.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(С) → C3 be a transformation such that T(а+ bx + сa) — (а, а + b, а +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(С) → C3 be a transformation such that T(а+ bx + сa) — (а, а + b, а +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,...

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