Finding Solutions to Systems of Linear Equations Using Reduced Echelon Form

[sheldonrocks97]

Homework Statement

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]

Homework Equations

None

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.

 

[Ray Vickson]

Homework Statement

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]

Homework Equations

None

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.

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.

 

[LCKurtz]

Homework Statement

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]

Homework Equations

None

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.

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.