A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

can anyone help me with proof that det(A)=det(-A) for nxn matrices?

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

    You can find it in any Linear Algebra book

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok I guess I'll look harder

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Which Linear Algebra book are you refering?

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I know we are using the scaling method three times which gives us det(B)=s(det(A))

  5. nowhereman
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you can find all you need here: http://en.wikipedia.org/wiki/Determinant Just use \[\det (αA) = α^n \det (A) \] and you will see your conjecture does only hold for even numbers n

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so does -1(det(A)=det(-A)

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ahh yes...I get it now, I overlooked that formula, the exponent threw me off, thakns

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    there are many ways to prove it, depends on how the determinant is defined. In beginning linear algebra book, the determinant is not defined using the Leibniz formula. In that case, there is another proof

  9. 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.