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Coordinates relative to a basis (linear algebra)

  1. Apr 7, 2010 #1
    1. The problem statement, all variables and given/known data
    The set B = {-4-x^2, -8+4x-2x^2, -14+12x-4x^2} is a basis for P2. Find the coordinates of p(x) = (-2 +0x -x^2) relative to this basis.


    2. Relevant equations
    n/a


    3. The attempt at a solution
    so the set would be in a matrix like this:
    |-4 0 -1|
    |-8 4 -2|
    |-14 12 -4| and multiplying this by

    |-2|
    | 0|
    |-1| as the vector for p(x) gives

    | 9|
    |18|
    |32| but that's not the right answer and I thought that's how you'd do it.
     
  2. jcsd
  3. Apr 7, 2010 #2

    Mark44

    Staff: Mentor

    You're going at this the wrong way around. You want the vector c = <c1, c2, c3>T such that Ac = <-2, 0, -1>T, where A is the matrix you have above.
     
  4. Apr 7, 2010 #3
    oh ok, so if multiply A inverse times <-2, 0, -1> would it be right? I tried that and got <-5/2, 1, 12> which I checked but is still the wrong answer. Did I just put the coordinates in the wrong order or something? because the inverse thing makes sense but it didn't accept my answer. thanks.
     
  5. Apr 7, 2010 #4

    Mark44

    Staff: Mentor

    Those aren't the right coordinates. The coordinates I got check.
     
  6. Apr 7, 2010 #5
    oh ok, I figured it out, thanks a lot!
     
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