Purchase Solution

Prove that the Kernel of a homomorphism is a subspace.

Not what you're looking for?

Ask Custom Question

Prove that the Kernel of a homomorphism is a subspace.

Purchase this Solution

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.

Solution Preview

Please see the attached file.

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 provided by:
Education
  • BSc, Manipur University
  • MSc, Kanpur University
Recent Feedback
  • "Thanks this really helped."
  • "Sorry for the delay, I was unable to be online during the holiday. The post is very helpful."
  • "Very nice thank you"
  • "Thank you a million!!! Would happen to understand any of the other tensor problems i have posted???"
  • "You are awesome. Thank you"
Purchase this Solution


Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.