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Linear algebra - coordinates.

  1. Mar 28, 2008 #1
    Can anyone explain exactly how you are supposed to apply coodinates in matrices? I am somewhat lost in class.

    For example say, i have the coordinates A =
    1 2
    0 2 --> this is a 2 X 2 matrix


    and I have to apply this to the basis

    B =
    1 0
    0 0,

    0 1
    0 0,

    0 1
    0 1


    -> The book gives the following matrix as the answer:

    1 0 0
    0 1 1
    0 0 1

    - But I still don't get how they got here. Can anyone outline the process?

    Thank you!
     
  2. jcsd
  3. Mar 29, 2008 #2

    HallsofIvy

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    No, I have no idea what you are talking about. (And I thought I knew a little about Linear Algebra!) I have never heard of "applying coordinates" to matrices, nor do I see how you are going from 2 by 2 matrices to a 3 by 3 matrix. Could you state the problem exactly as it is given?
     
  4. Mar 29, 2008 #3
    I am sorry, this is supposed to be a change of basis problem. We are changing B to basis A.

    Can you help?
     
  5. Mar 29, 2008 #4
    we are trying to find the change of basis matrix.
     
  6. Mar 29, 2008 #5

    HallsofIvy

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    From what basis to what basis? And what space? The matrices you list as a basis are NOT a basis for M4, because there are only 3 of them.
     
  7. Mar 29, 2008 #6
    from B to A. Please help me. The question asks for the change of basis matrix.

    No other info is given.
     
  8. Mar 29, 2008 #7
    Please help me brothers.
     
  9. Mar 29, 2008 #8

    HallsofIvy

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    Honestly, the problem, as you stated it, still makes no sense to me. You have given us 3 matrices which you say is a basis (of what space? The space of all 2 by 2 matrices is 4 dimensional so it can't have a basis of 3 matrices) and ask for a "change of basis matrix". What is the basis to change to?
     
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