A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Let U and V be subspaces of a vector space W. Prove that their intersection is also a subspace of W

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Let X be the intersection of U and V. 1) X closed under addition: Assume x in X and y in X. From this, we know x in U and y in U. But since we know that U is a subspace, x+y in U holds. Similarly, one can show that x+y in V and therefore x+y in X. So X is indeed closed under addition. 2) X closed under scalar multiplication: ------------------------------------------ Assume x in X and r in R. Again, we know x in U. Since U is a subspace, it is closed under scalar multiplication. Therefore, r*x in U holds. Also r*x in V holds with a similar argument. From this r*x in X follows. So X is closed under scalar multiplication. Therefore by subspace theorem, we're done. You can use the definitely of a vectorspace as well, but that's more tedious.

  2. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.