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

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Homework Statement



Prove the thread title.

Homework Equations



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

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!
 
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Well what will it mean if you subtract identical row 1 from the other identical row?
 
rock.freak667 said:
Well what will it mean if you subtract identical row 1 from the other identical row?

One of the rows will now be zero
 
infinitely many solutions to what?
 
lanedance said:
infinitely many solutions to what?

Ax = 0 where A is an n x n matrix
 
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?
 
n - 1 equations and n variables ... meaning an infinite number of solutions.
 
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