System of equations, matrices

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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?


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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.
 

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Dick
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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?
 

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