# System of equations, matrices

In summary, the conversation discusses a linear system with four equations and three unknowns that has a unique solution. The rref of the coefficient matrix is shown for a system with three equations and three unknowns. It is noted that a system with four equations and three unknowns has an additional row with all zeros, indicating multiple solutions. The conversation ends with a question about the rref of a specific system with a unique solution.

## 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?

## 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.

## 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?

## 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.