Cramer's Rule

The technique used to solve systems of linear equations using determinants is called Cramer’s rule. The values of the variables can be determined by the determinants. Here, one determinant is derived from the number set in front of the variables, which is known as the coefficient matrix, and the other comes from changing one column from the matrix with the numbers following the equal signs (the answer column). After that, to find the value of a variable, divide the two determinants.  

Let us see how Cramer’s rule works in the following system of equations: 

        2x + y + z = 3
        x - y - z = 0 
        x + 2y + z = 0

Write the given equations with all coefficients:

       2x + 1y + 1z = 3
       1x - 1y - 1z = 0 
       1x + 2y + 1z = 0

Create the coefficient matrix and identify its determinant (D):