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Basis of a vector space

  1. Apr 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Determine whether the following 2 x 2 matrices form a basis of the vector space M2x2(R) of all (2x2)-matrices over R:

    A1=
    1 0
    0 0

    A2=
    2 2
    0 0

    A3=
    3 2
    1 0

    A4=
    4 3
    2 1

    2. Relevant equations



    3. The attempt at a solution

    So for them to be bases, they must be a linearly independant set that spans the vector space. How can i go about showing this for each matrix?
     
  2. jcsd
  3. Apr 13, 2008 #2

    Hurkyl

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    The question asked if those vectors form a basis. The question didn't ask if each individual vector was a basis (such a question wouldn't even make sense).
     
  4. Apr 13, 2008 #3
    Do i need to show that each matrix is invertible?
     
  5. Apr 13, 2008 #4

    Hurkyl

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    I think you need to start with the definitions, to make sure you understand just what the question is asking.
     
  6. Apr 13, 2008 #5
    Oh so a1...a4 must all be linealry independant?
     
  7. Apr 13, 2008 #6

    Hurkyl

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    Yes, that is what you need to show.
     
  8. Apr 13, 2008 #7
    Thanks, library closes now and no internet at new flat :cry:
     
  9. Apr 13, 2008 #8

    Dick

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    Try to solve c1*A1+c2*A2+c3*A3+c4*A4=0. It's pretty easy. What are the solutions for c1...c4? What does that say about linear independence?
     
  10. Apr 13, 2008 #9
    Hi, If I have a question i post it here and you will respond (if you are on line)?
     
  11. Apr 13, 2008 #10
    Hi DIck can you help me with this problem..."find the determinant of the linear transformation T(M)=[1,2,2,3]M+M[1,2,2,3] from the space V of symmetric 2x2 matrices to V
     
  12. Apr 13, 2008 #11

    Dick

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    In the future, always post a new thread for a new problem, ok? Otherwise this will get buried and not enough people will see it. The answer to your question is not obvious to me, maybe somebody else knows.
     
  13. Apr 13, 2008 #12
    hi dick thank you for responding. i posted a new thread. if i have to log off how will i be able to find it again? a response will be in my email box? i don't know how this forum works are there instructions somewhere?
     
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