# Associated Homogeneous System definition

1. Aug 19, 2010

### Zeato

Hi, thank you for viewing this thread. I have been googling for its definition for quite a while, but have not found any yet. Just wondering if there is a definition of it, in mathematical notations and in words?

2. Aug 19, 2010

### HallsofIvy

Any system of linear equations can be written in the form
$$a_{11}x_1+ a_{12}x_2+ \cdot\cdot\cdot+ a_{1n}x_n= b_1$$
$$a_{21}x_1+ a_{22}x_2+ \cdot\cdot\cdot+ a_{2n}x_n}= b_2$$
etc.

That is, the left side of each equation is a linear combination of the variables, and the right side is a number. The "associated homogenous system" is exactly the same with the numbers on the right side all set to 0.

The "associated homogenous system" for the above system is:
$$a_{11}x_1+ a_{12}x_2+ \cdot\cdot\cdot+ a_{1n}x_n= 0$$
$$a_{21}x_1+ a_{22}x_2+ \cdot\cdot\cdot+ a_{2n}x_n= 0$$
etc.

Last edited by a moderator: Aug 19, 2010
3. Aug 19, 2010

### Zeato

Alright, I got it. Thanks for your help!