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Linear System problem

  1. Feb 4, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose that Gaussian Elimination gives the soluiton of a Linear System Ax=c as x = x0 + a1x1 + a2x2, where A is a 6X6 matrix and a1 and a2 are arbitrary. Is the matrix A invertible? Explain

    3. The attempt at a solution

    I simply explained that due to properties of an invertible matrix, Ax=c must have exactly one solution but if a1 and 2 are arbitrary, then x = x0 + a1x1 + a2x2 has infinitely many solutions and A cannot be invertible

    does anyone agree with this answer and if not, any advice on how to start the problem would be great appreciated :redface: thanks a lot!
  2. jcsd
  3. Feb 5, 2010 #2


    Staff: Mentor

    I'm assuming that x0, x1, and x2 are vectors. Your reasoning looks fine to me. If A had been invertible then you would have gotten a unique solution, which could be written as x = A-1c.
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