Answered: Suppose V is finite-dimensional and dim…

Suppose V is finite-dimensional and dim V > 1. Prove that the set of noninvertible operators on V is not a subspace of L(V).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 10EQ

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2 Suppose V is finite-dimensional and dim V > 1. Prove that the set of
noninvertible operators on V is not a subspace of L(V).

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