# Reduced echelon form?

1. Feb 16, 2014

### sheldonrocks97

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

In each part, the reduced echelon form of the augmented matrix of a system of linear
equations is given. Find all solutions to the original system.
a.

[1 0] [2]
[0 1] [5]

b.

[1 0] [2]
[0 0] [1]

c.

[1 0] [2]
[0 0] [0]

d.

[1 2 0 1] [2]
[0 0 1 1] [5]

2. Relevant equations

None

3. The attempt at a solution

I know that a.) is already in reduced row echelon form. I just don't understand how to get the last four, because the second and third don't have ones other than in 1 corner.

2. Feb 16, 2014

### Ray Vickson

Write out the actual equations corresponding to the echelon forms; after all, that is what we use such form for in the first place---to stand as shorthand for some equations.

3. Feb 16, 2014

### LCKurtz

You don't "get" the last four into row echelon form. They are also given to already be in row echelon form. You are just asked to write out the solutions.