# Homework Help: System of linear equations

1. Feb 14, 2007

### EvLer

1. The problem statement, all variables and given/known data

is every system of 6 equations and 5 unknowns consistent?

I think that not every one is consistent because after Gaussian elimination you may arrive at equation where 0=1, but I want a sure confirmation.
Thanks

2. Feb 14, 2007

### e(ho0n3

What does it mean for a system of linear equations to be consistent? Does your answer agree with the definition?

3. Feb 14, 2007

A trivial example:

x1 + x2 + x3 + x4 + x5 = 1
x1 + x2 + x3 + x4 + x5 = 0
x1 + x2 + x3 + x4 + x5 = 0
x1 + x2 + x3 + x4 + x5 = 0
x1 + x2 + x3 + x4 + x5 = 0
x1 + x2 + x3 + x4 + x5 = 0

Does this system have a solution?

Edit: I forgot to add the 6th equation. The question remains unchanged.

Last edited: Feb 14, 2007
4. Feb 14, 2007

### EvLer

thanks.
ps: sorry, perhaps I made a mistake: 6 equations IN 5 unknowns.

5. Feb 14, 2007

### HallsofIvy

That was what everyone assumed you meant, that is what radou gave.