1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Finding the Dimension and Basis of the Matrix Vector space

  1. Oct 14, 2012 #1
    1. The problem statement, all variables and given/known data
    The set K of 2 × 2 real matrices of the form [a b, -b a] form a field with the usual operations.
    It should be clear to you that M22(R) is a vector space over K. What is the dimension of M22(R) over K? Justify your answer by displaying a basis and proving that the set displayed is actually a basis.

    2. Relevant equations

    3. The attempt at a solution

    I don't think there can be a basis over the field K, because no linear combination of the matrices [a b, -b a] with any M22 can form, say [1 0, 0 0]. Which would be in M22. Any help would be greatly appreciated. Thanks!
  2. jcsd
  3. Oct 16, 2012 #2
    Could you do a combination say (0 a, 0 -b) (0 -b, 0 a), (a 0, b 0), (-b 0, a 0)? Could this form a basis? Or does it have to be real integers? thanks
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook