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

1. Jul 5, 2011

Jamin2112

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. Jul 5, 2011

rock.freak667

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

3. Jul 5, 2011

Jamin2112

One of the rows will now be zero

4. Jul 5, 2011

lanedance

infinitely many solutions to what?

5. Jul 5, 2011

Jamin2112

Ax = 0 where A is an n x n matrix

6. Jul 5, 2011

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?

7. Jul 6, 2011

Jamin2112

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