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An n x n matrix with two identical rows has infinitely many solutions

  1. Jul 5, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove the thread title.

    2. Relevant equations

    Without using anything about rank, nullity, etc., --- just row reduction

    3. The attempt at a solution

    Can't figure this out. It's actually a friend one of my buddies is doing for his class. PLEASE ANSWER IN LESS THAN 2 HOURS! IT'S URGENT!
     
  2. jcsd
  3. Jul 5, 2011 #2

    rock.freak667

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    Well what will it mean if you subtract identical row 1 from the other identical row?
     
  4. Jul 5, 2011 #3
    One of the rows will now be zero
     
  5. Jul 5, 2011 #4

    lanedance

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    infinitely many solutions to what?
     
  6. Jul 5, 2011 #5
    Ax = 0 where A is an n x n matrix
     
  7. Jul 5, 2011 #6

    ideasrule

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    OK, so one of the rows is now zero, meaning the only information it gives us is 0=0. How many equations do you now have, and in how many variables?
     
  8. Jul 6, 2011 #7
    n - 1 equations and n variables .......... meaning an infinite number of solutions.
     
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