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Linear Algebra - Determining a Solution to AX = B

  1. Jun 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Assume that

    [tex] A \left( \begin{array}{c} 1 \\ -1 \\ 2 \end{array} \right) = 0 = A \left( \begin{array}{c} 2 \\ 0 \\ 3\end{array} \right) [/tex]

    and that AX = B has a solution [tex] Xo= \left( \begin{array}{c} 2 \\ -1 \\ 3 \end{array} \right) [/tex]

    Find a two parameter family of solutions to AX = B

    2. Relevant equations

    AX = B

    [tex] A \left( \begin{array}{c} 1 \\ -1 \\ 2 \end{array} \right) = 0 = A \left( \begin{array}{c} 2 \\ 0 \\ 3\end{array} \right) [/tex]


    3. The attempt at a solution

    Representing coefficient columns of matrix A as a (A1 , A2 , A3) for corresponding n-vectors of x,

    A1 - A2 + 2A3 = 2A1 + 3A3

    A2 = -A1 - A3

    not sure where to go from here or really what i am doing.
     
    Last edited: Jun 6, 2012
  2. jcsd
  3. Jun 6, 2012 #2

    vela

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    This is more of a conceptual problem. Think about things like the homogeneous solution, particular solution, null space, etc.
     
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