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Homework Help: Linear Transformation / Coordinate Vector Question

  1. Apr 6, 2010 #1
    1. The problem statement, all variables and given/known data
    The following vectors form an ordered basis E = [v1, v2] of the subspace V = span(v1,v2):

    v1 = (1,2,1)^T , v2 = (3,2,1)^T.

    The vector v = (24,-8,-4)^T belongs to the subspace V. Find its coordinates (c1,c2)^T = [v]E relative to the ordered basis E = [v1,v2].

    2. Relevant equations


    3. The attempt at a solution

    I am not quite sure how to approach this problem. I wanted to calculate the inverse of:

    1 3
    2 2
    1 1

    and then multiply v = (24, -8, -4)^T by the inverse to get the coordinate vector relative to E, however I have no idea if that is the right approach. I feel I'm missing something...
  2. jcsd
  3. Apr 6, 2010 #2


    Staff: Mentor

    The only matrices that have inverses are square matrices. The one you show above is 3 x 2, so isn't square.
    Solve the equation below for the constants c1 and c2.
    (24, -8, -4)^T = c1*(1,2,1)^T + c2*(3,2,1)^T
  4. Apr 6, 2010 #3
    Oh, wow. Thank you, it seems I was over-complicating things...the wording of that problem had my brain in knots.
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