# System of Three Linear Equations in Matrix Form

In this tutorial we shall discuss a system of three linear equations in matrix form.

__A System of Three Linear Equations__

Consider the system of three equations of straight lines is given as

Equations (i), (ii) and (iii) are linear equations and three variables, and . can be written in matrix form as follows:

Equation (i) becomes

It can be further written as

Here is the coefficient matrix and is the variable matrix.

We have already discussed that the three lines (i), (ii) and (iii) will be concurrent if

This shows that the given lines (i), (ii) and (iii) will be concurrent if the coefficient matrix is singular.