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.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 69E: Find a basis for R2 that includes the vector (2,2).

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