# 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

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.