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

[Jamin2112]

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!

 

[rock.freak667]

Well what will it mean if you subtract identical row 1 from the other identical row?

 

[Jamin2112]

Well what will it mean if you subtract identical row 1 from the other identical row?

One of the rows will now be zero

 

[lanedance]

infinitely many solutions to what?

 

[Jamin2112]

infinitely many solutions to what?

Ax = 0 where A is an n x n matrix

 

[ideasrule]

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?

 

[Jamin2112]

n - 1 equations and n variables ... meaning an infinite number of solutions.