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Homework Help: Homogeneous linear system

  1. Aug 2, 2008 #1
    I have a question:
    If the vectors of v & u are solutions of the nonhomogeneous linear system Ax=b, then ru+sv is a solution of the nonhomogeneous system for any real values of r and s.
    is this statement true?
    is this statement true for homogeneous systems too?
  2. jcsd
  3. Aug 2, 2008 #2
    Hint: When a nonhomogeneous linear system has infinite solutions, then the general solutions can be written in parametric vector form.

    This can be used to answer both questions.
  4. Aug 2, 2008 #3


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    Homework Helper

    You should be able to find a counterexample easily for the first question. For the second, try writing the matrix equation for Ax=b using ru+sv.
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