Using determinate to solve simultaneous equations
Linear Equations: Solutions Using Determinants with Three Variables The determinant of a 2 × 2 matrix is defined as follows: The determinant of a 3 × 3 matrix can be defined as shown in the following. Each minor determinant is obtained by crossing out the first column and one row. Example 1 Evaluate the following determinant. First find the minor determinants. The solution is To use determinants to solve a system of three equations with three variables (Cramer's Rule), say x , y , and z , four determinants must be formed following this procedure: Write all equations in standard form. Create the denominator determinant, D , by using the coefficients of x , y , and z from the equations and evaluate it. Create the x ‐numerator determinant, D x , the y ‐numerator determinant, D y , and the z ‐numerator determinant, D z , by replacing the respective x , y , and z coefficients with the constants from the e