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Coordiante Vector

  1. Oct 14, 2005 #1
    How do you find the coordinate vector of

    A =
    1 1
    1 2
    2 2

    relatvie to the basis {A_1, A_2, A_3, A_4, A_5, A_6}?

    A_1 =
    3 6
    3 -6
    0 0

    A_2 =
    0 -1
    -1 0
    1 1

    A_3 =
    0 -1
    -2 -2
    2 1

    A_4 =
    1 0
    1 3
    0 2

    A_5 =
    1 0
    0 1
    2 2

    A_6 =
    2 0
    1 4
    -1 3

    Is it jus taking each of the matrix and making one large one and doing rref so I get:

    88/157(A_1) + 23/157(A_2) + etc...?

    I don't think its working out though...not even sure if its the correct thing to do...thanks
     
  2. jcsd
  3. Oct 14, 2005 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    If I understand your notation correctly, you are looking for numbers x1, x2,..., x6 so that
    x1A1+ x2A2+ ...+ x2A2= A.

    Looking at the individual components, that gives
    3x1+ x4+ x5+ 2x6= 1,
    6x1- x2- x3= 1, etc.
    6 equations in 6 unknowns. Of course, you can set that up as a matrix equation itself.
     
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