# Prove that the Kernel of a homomorphism is a subspace.

Prove that the Kernel of a homomorphism is a subspace.

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Modern Algebra

Vector Spaces and Modules (III)

Homomorphism of two vector spaces

Kernel of a homomorphism

By:- Thokchom Sarojkumar Sinha

Prove that the Kernel of a homomorphism is a subspace.

Solution:- Let be a homomorphism of into where and are vector spaces over the field .

We have to prove that

Ker is a subspace ...

#### Solution Summary

This solution is comprised of a detailed explanation of the Kernel of a homomorphism.

It contains step-by-step explanation to prove that the Kernel of a homomorphism is a subspace.

Notes are also given at the end.

Solution contains detailed step-by-step explanation.