Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

TomLikesPhysics

  • 3 years ago

I have 4 different vectors with 5 components. What is the fastest way to determine if these vectors form a linearly independent base in 5-dim space?

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

    4 vectors can't form a base in 5-dim space. You need at least 5 vectors

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

    Of course... Well, how do I check if 5 vectors with 5 components form a linearly independet base? Let´s say it is not obvious and there is not a vector who looks like a multiple of another vector.

  3. myko
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    check determinant of matrix formed by this vectors. If it's equals 0 vectors are dependent. If not - independent.

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

    Oh, I did not know that I can use a determinant with vectors which are in a higher dim. than 3. Thx for your help myko!

  5. myko
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you can do it in any dimention. The only thing you need is the matrix to be square

  6. 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