Suppose T:R³→R³ is the transformation given below. Determine whether T is one-to-one and/oronto. If it is not one-to-one, show this by providing two vectors that have the same image under T.If I is not onto, show this by providing a vector in R³ that is not in the range of T.5x1-5x23x1-3x2x0-3x1+3x2xoTx1x2T is not one-to-one:ΤΟ0=0and TT is not onto:00000 is not the image of any x under T.0

The give linear transformation T:ℝ3→ℝ3 is defined by Tx0x1x2=5x1-5x23x1-3x2x0-3x1+3x2

Suppose T:R³→R³ is the transformation given below. Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two vectors that have the same image under T. If T is not onto, show this by providing a vector in R³ that is not in the range of T. 5x1-5x2 3x1-3x2 *20-3x+3x2 xo Tx1 T is not one-to-one: 0 0 0 and TO 0 0 T is not onto: 0 0 0 is not the image of any x under T. 0

Suppose T:R³→R³ is the transformation given below. Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two vectors that have the same image under T. If T is not onto, show this by providing a vector in R³ that is not in the range of T. 5x1-5x2 3x1-3x2 *20-3x+3x2 xo Tx1 T is not one-to-one: 0 0 0 and TO 0 0 T is not onto: 0 0 0 is not the image of any x under T. 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 3EQ

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