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Linear Algebra: Projection onto a subspace

  1. Aug 1, 2010 #1
    1. The problem statement, all variables and given/known data

    mat.png

    That is the question. The answer on the bottom is incorrect

    2. Relevant equations

    20276.nce108.gif
    I believe that is the formula that is supposed to be used.

    3. The attempt at a solution

    All I really did was plug in the equation into the formula but there is something I am missing because the answer is incorrect

    Projection = (41/65)v1 + (26/5)v2
    This is what I got after inserting the projection formula.
    And in the first image, on the bottom it shows the final solutions I got.


    Please help me figure out how to do this question and where I went wrong.

    Thanks in advanced!
     
  2. jcsd
  3. Aug 1, 2010 #2
    Just a thought, but do you have to provide the solutions in a specific number format (i.e. rounded to a certain number of figures) or maybe as exact fractions?
     
  4. Aug 1, 2010 #3
    I don't think it's important, no. =)
     
  5. Aug 1, 2010 #4

    vela

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    What conditions must v1 and v2 meet so that the formula can be used?

    An alternative approach would be to find a vector x that's perpendicular to V, and find the projection of v onto x, and subtract that from v. What's left over will lie in the subspace V.
     
  6. Aug 2, 2010 #5
    Apparently the problem is that it's not orthogonal.
     
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