Suppose T: M2.2 R4 is a linear transformation whose action on a basis for M2.2 is as follows: -2 3 -3 1 10 1 1 T 11 1 1 3 -3 T -4 5 -1 3 0 2 1 -4 0 0 1 -3 6. -5 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 vector in R4 that is not in the image of T. T is not one-to-one: 0 0 0 0 and T 0 0 0 0 T is not onto: is not the image of any matrix under T.

Suppose T: M2.2 R4 is a linear transformation whose action on a basis for M2.2 is as follows: -2 3 -3 1 10 1 1 T 11 1 1 3 -3 T -4 5 -1 3 0 2 1 -4 0 0 1 -3 6. -5 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 vector in R4 that is not in the image of T. T is not one-to-one: 0 0 0 0 and T 0 0 0 0 T is not onto: is not the image of any matrix under 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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