What Does the RREF of a 4x3 Matrix with a Unique Solution Look Like?

[maximade]

Homework Statement

Consider a linear system of four equations with three unknowns. We are told that the system has a unique solution. What does the rref of the co efficient matrix look like?

Homework Equations

The Attempt at a Solution

When it says "unique solution" I'm going to guess it means it has 1 solution.
Correct me if I'm wrong but, I believe that a system of 3 equations with 3 unknowns that has a unique solution will look like this:
[ 1 0 0 l x
0 1 0 l y
0 0 1 l z]

But for a system that has 4 equations with three unknowns, would it look like this:
[ 1 0 0 l x
0 1 0 l y
0 0 1 l z
0 0 0 l k] ?
This is what gets me, when a row has all 0's it means that it has multiple solutions.
Thanks in advance.

 

[Dick]

Homework Statement

Consider a linear system of four equations with three unknowns. We are told that the system has a unique solution. What does the rref of the co efficient matrix look like?

Homework Equations

The Attempt at a Solution

When it says "unique solution" I'm going to guess it means it has 1 solution.
Correct me if I'm wrong but, I believe that a system of 3 equations with 3 unknowns that has a unique solution will look like this:
[ 1 0 0 l x
0 1 0 l y
0 0 1 l z]

But for a system that has 4 equations with three unknowns, would it look like this:
[ 1 0 0 l x
0 1 0 l y
0 0 1 l z
0 0 0 l k] ?
This is what gets me, when a row has all 0's it means that it has multiple solutions.
Thanks in advance.

x=1, y=2, z=3 and x+y=3 has a unique solution. What does it's rref look like?