Consistency of 6x5 Linear Systems: A Scientific Perspective

[EvLer]

Homework Statement

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

 

[e(ho0n3]

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.

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

 

[radou]

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.

 

[EvLer]

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

 

[HallsofIvy]

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