by Prove: If the module MR if finitely generated then every proper submodule of M is contained in a maximal submodule of M. ✓ Let V = VR be a vector space with basis ((1,0), (0,1)). Let a: V → V defined as follows: a((a, b)) = (a,0), V (a, b) EЄ V. Then answer the following (1) Prove that a is a module homomorphism. (2) Find Ker(a). (3) Show that Ker(a) is a direct summand of V.

by Prove: If the module MR if finitely generated then every proper submodule of M is contained in a maximal submodule of M. ✓ Let V = VR be a vector space with basis ((1,0), (0,1)). Let a: V → V defined as follows: a((a, b)) = (a,0), V (a, b) EЄ V. Then answer the following (1) Prove that a is a module homomorphism. (2) Find Ker(a). (3) Show that Ker(a) is a direct summand of V.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 33EQ

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