Suppose T: P2→M2,2 is a linear transformation whose action on a basis for P2 is as follows: 2 -1 -1 3 4-2 -2 6 2-2 -4 4 T(x²+x+1)= T(2x²+x+1)= Give a basis for the kernel of T and the image of T by choosing which of the original vector spaces each is a subset of, and then giving a set of appropriate vectors. If one of your bases contains polynomials, give your answer as a comma-separated list of polynomials, using the '^' character to indicate an exponent and x as the variable, e.g. 5x^2-2x+1 Basis of Kernel is a Subset of P2 Bker = {0} T(1) = Basis of Image is a Subset of P2 Bim = {0}

Suppose T: P2→M2,2 is a linear transformation whose action on a basis for P2 is as follows: 2 -1 -1 3 4-2 -2 6 2-2 -4 4 T(x²+x+1)= T(2x²+x+1)= Give a basis for the kernel of T and the image of T by choosing which of the original vector spaces each is a subset of, and then giving a set of appropriate vectors. If one of your bases contains polynomials, give your answer as a comma-separated list of polynomials, using the '^' character to indicate an exponent and x as the variable, e.g. 5x^2-2x+1 Basis of Kernel is a Subset of P2 Bker = {0} T(1) = Basis of Image is a Subset of P2 Bim = {0}

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 31EQ

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