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Let V be a n-dimensional vector space, L : V → V be a linear transformation. Which of the following statements is correct? L is 1-1 implies L is onto, but not vice versa L is onto implies L is 1-1, but not vice versa L is 1-1 if and only if L is onto There is no relationship between L being 1-1 and L being onto.

Let V be a n-dimensional vector space, L : V → V be a linear transformation. Which of the following statements is correct? L is 1-1 implies L is onto, but not vice versa L is onto implies L is 1-1, but not vice versa L is 1-1 if and only if L is onto There is no relationship between L being 1-1 and L being onto.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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Let V be a n-dimensional vector space, L : V → V be a linear transformation. Which of the following statements is correct? L is 1-1 implies L is onto, but not vice versa L is onto implies L is 1-1, but not vice versa L is 1-1 if and only if L is onto There is no relationship between L being 1-1 and L being onto.
Transcribed Image Text:Let V be a n-dimensional vector space, L : V → V be a linear transformation. Which of the following statements is correct? L is 1-1 implies L is onto, but not vice versa L is onto implies L is 1-1, but not vice versa L is 1-1 if and only if L is onto There is no relationship between L being 1-1 and L being onto.
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