non-homogeneous and homogeneous?

In general, a system with m linear equations and n unknowns can be written as


圖片參考：http://upload.wikimedia.org/math/b/5/d/b5d3f5e8dd6afaad98f3450705efad39.png

where
圖片參考：http://upload.wikimedia.org/math/b/b/2/bb2e29f345710185429f7090ce3d3c44.png
are the coefficients of the system. We can collect the coefficients in a matrix as follows:


圖片參考：http://upload.wikimedia.org/math/3/c/e/3cebfd7fac01b208d18a8fe56d6e1fea.png

If we represent each matrix by a single letter, this becomes


圖片參考：http://upload.wikimedia.org/math/2/9/9/299e5c6fa6afd1ff13210c9a5d905971.png

where A is an m×n matrix, x is a column vector with n entries, and b is a column vector with m entries.
A system of the form


圖片參考：http://upload.wikimedia.org/math/f/a/b/fab56c2fd8f5b1af16d0401b34eab505.png

is called a homogeneous system of linear equations. Otherwise, A system is called a non-homogeneous system of linear equations

There are many mathematical system is " homogeneous " . You have not clarified what are you going to ask but someone ANSWERED you quickly.
This is very interesting!
Hope you really understand what is " HOMOGENEOUS " but not just copying.