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

__A System of Three Linear Equations__**:**

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

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

Now equation (i) becomes

It can be further written as

Where is the coefficient matrix and is 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.