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Showing nonsingular matrix has a unique solution

  1. Jan 12, 2013 #1
    1. The problem statement, all variables and given/known data
    It states that for any linear system with a nonsingular matrix of coefficients has solution and its solution is unique.

    2. Relevant equations



    3. The attempt at a solution
    I wanted to put an diagram of an arbitrary nxn matrix showing it has unique solution but I'm not sure how to represent a nxn matrix in echelon form?
     
    Last edited: Jan 12, 2013
  2. jcsd
  3. Jan 13, 2013 #2
    correct...The problem says (i think which you are trying to prove) that it has a solution and the solution is unique. So you know that the matrix of the arbitrary nxn matrix will have a pivot and ever row and column. To represent that use the given that it is a linear system with nonsingular matrix of coefficients. I've never seen the description as "non singular" before but I assume it relates to the fact that the matrix will be isomorphic to r^n
     
  4. Jan 13, 2013 #3
    Oh ok. I assume its OK to use explain it using the assumption the matrix is nonsingular(means it has at one solu ion).
     
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