Suppose T: R³→P2 is a linear transformation whose action is defined by a Tb с = (3a-3b+3c)x²+(2a-2b+2c)x+(a-b+c) Give a basis for the kernel of I 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 Basis of Image is a Subset of R³ Number of Vectors: 1 Bim = 0

Suppose T: R³→P2 is a linear transformation whose action is defined by a Tb с = (3a-3b+3c)x²+(2a-2b+2c)x+(a-b+c) Give a basis for the kernel of I 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 Basis of Image is a Subset of R³ Number of Vectors: 1 Bim = 0

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 6EQ

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