System of linear equations
Let
denote a
field,
and let
for
and
.
We call
-
a
(homogeneous)
system of linear equations in the variables
. A tuple
is called a solution of the linear system if
holds for all
.
If
is given,[1]
then
-
is called an inhomogeneous system of linear equations. A tuple
is called a solution to the inhomogeneous linear system if
holds for all
.
- ↑ Such a vector is sometimes called a disturbance vector of the system.