a system of linear equations (or a linear system) is a collection of one or more linear equations involving the same variables.
An example of a linear system is the following:
The coefficients of the left side can be written as
The other side of the equation can be represented using the column vector
The variables can then be represented using a column vector as well
This means the linear system can also be expressed using matrices as follows
In this example the matrices are being multiplied using the dot product
Usually this linear system is just written simply as
Linear systems which have no-solutions are called inconsistent, conversely they're called consistent if they have at least one solution.
Solving linear systems can be done in a variety of ways