# Echelon Form

• Mar 31st 2008, 09:13 PM
ah-bee
Echelon Form
What is the precise definition of a non-square matrix in echelon form? Say we have something like:

1, 2, 3, 4, 5, 6 | 7
2, 3, 4, 5, 6 ,7 | 8
3, 4 ,5, 6, 7, 8 | 9

How would the echelon form of that look like? Don't worry about explaining that set of equations having so and so amount of parameters and infinite solutions. I'm just wondering how the echelon form of a non-square matrix is defined.

• Mar 31st 2008, 09:18 PM
mr fantastic
Quote:

Originally Posted by ah-bee
What is the precise definition of a non-square matrix in echelon form? Say we have something like:

1, 2, 3, 4, 5, 6 | 7
2, 3, 4, 5, 6 ,7 | 8
3, 4 ,5, 6, 7, 8 | 9

How would the echelon form of that look like? Don't worry about explaining that set of equations having so and so amount of parameters and infinite solutions. I'm just wondering how the echelon form of a non-square matrix is defined.

It might look something like

* * * * * * | *
0 0 * * * * | *
0 0 0 0 0 * | *

for example where * denotes non-zero entries.
• Mar 31st 2008, 09:29 PM
ah-bee
does that rule hold for every non-square matrix though? having the last row in the matrix being zeros except for the last term and is there any restrictions to how many zeros u can have in the preceding row? in your case u have used 0 0 **** but not 0 0 0 ***, why is this?
• Apr 1st 2008, 02:01 AM
mr fantastic
Quote:

Originally Posted by ah-bee
does that rule hold for every non-square matrix though? having the last row in the matrix being zeros except for the last term and is there any restrictions to how many zeros u can have in the preceding row? in your case u have used 0 0 **** but not 0 0 0 ***, why is this?

It was only an example. I assumed you understood the technical definition of row echelon form - read this.