If a linear transformation L: R → R is one-to-one, thenO The rank is two and the nullity is three.O The rank and nullity can be any pair of non-negative numbers thatadd up to three.O The situation is impossibie.O The rank is three and the nullity is two.

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Answered: If a linear transformation L : R →R' is…

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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If a linear transformation L : R R is one-to-one, then O The rank and nullity can be any pair of non-negative numbers that add up to three. O The rank is three and the nullity is two. O The rank is three and the nullity is zero. O The situation is impossible.
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If a linear transformation L : R →R' is one-to-one, then O The rank is two and the nullity is three. O The rank and nullity can be any pair of non-negative numbers that add up to three. O The situation is impossible. O The rank is three and the nullity is two.