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Homework Help: Construct a 2 by 3 system that has these particular and homogeneous eq

  1. Feb 25, 2013 #1


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    1. The problem statement, all variables and given/known data
    Construct a 2 by 3 system Ax = b with particular solution xp = (2,4,0) and homogeneous solution xn = any multiple of (1,1,1).

    The answer is {{1,0,-1},{0,1,-1}} x = {{2},{4}} which has xp and xnull = (c,c,c).

    2. Relevant equations
    Ax = b

    3. The attempt at a solution
    I tried putting (2,4,0) as row 1 and (1,1,1) as row 2 and then reducing, I get {{1,0,2},{0,1,-1}} but, that doesn't seem to match up with the answer.

    Could someone please tell me how to do such a problem?

    Any input would be greatly appreciated!
  2. jcsd
  3. Feb 25, 2013 #2


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    2017 Award

    Staff: Mentor

    Re: Construct a 2 by 3 system that has these particular and homogeneou

    Similar to solving those problems, it is useful to begin with the homogeneous solution. The particular solution can be added afterwards.

    One possible answer.
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