Suppose T: M2,2-P2 is a linear transformation whose action on a basis for M22 is as follows: 0 1 00 11 11 -1 -1 -2 -1 4x²+2x+1 7-8-9- T -2x²-2x-2 00 Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two matrices that have the same image under T. If T is not onto, show this by providing a polynomial in P2 that is not in the image of T. Use the character to indicate an exponent and x as the variable for polynomials, e.g. 5x^2-2x+1 T -x²+x+2 T T is one-to-one T is onto = -x²+x+2 T = =

Suppose T: M2,2-P2 is a linear transformation whose action on a basis for M22 is as follows: 0 1 00 11 11 -1 -1 -2 -1 4x²+2x+1 7-8-9- T -2x²-2x-2 00 Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two matrices that have the same image under T. If T is not onto, show this by providing a polynomial in P2 that is not in the image of T. Use the character to indicate an exponent and x as the variable for polynomials, e.g. 5x^2-2x+1 T -x²+x+2 T T is one-to-one T is onto = -x²+x+2 T = =

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 3EQ

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