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Confirm the row vectors of A are orthogonal to the solution vectors?

  1. Jun 16, 2012 #1
    HI there. I'm taking Linear Algebra classes right now and this question has been bugging me.

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

    Find a general solution to the system, state the dimension of the solution space, and confirm the row vectors of A are orthogonal to the solution vectors.

    The given system is:
    (x1) + (x2) + (x3) = 0
    2(x1) + 2(x2) + 2(x3) = 0
    3(x1) + 3(x2) + 3(x3) = 0


    3. The attempt at a solution

    This last part about confirming vectors are orthogonal (bolded) confuses me. I have found the general solution can be written as

    (x1) = t + s
    (x2) = t
    (x3) = s

    And that the dimension of the solution is 2, since there are two vectors. But I do not understand how to do the last part of the question. What is it asking? Any guidance would be appreciated.
     
  2. jcsd
  3. Jun 16, 2012 #2

    LCKurtz

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    Your "solution" doesn't work in the first equation (nor the others).
     
  4. Jun 16, 2012 #3

    vela

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    The system can be written as a matrix multiplication Ax=0. A row vector is simply a row of the matrix A. You want to show that each of these row vectors is perpendicular to the solution x. As LCKurtz noted, you need to get that right first.
     
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