Cramer's Rule

Cramer's rule is used to solve systems of linear equations. It applies to systems that meet the following conditions:

The number of equations equals the number of unknowns.

The determinant of the coefficient matrix is nonzero.

Cramer's Rule

Δ is the determinant of the coefficient matrix.

Determinant of the Coefficient Matrix

And they are:

Δ 1, Δ 2 , Δ 3 ... , Δ n

Determinants are obtained by replacing the coefficients of the 2nd member (independent terms) in the 1st, 2nd, 3rd and the nth column, respectively.

The system solution is given by the following expressions:

System Solution

System Solution

System Solution

System Solution

System Solution

Examples

1 System of Equations

System Operations

System Operations

System Solution


2 System of Equations

System Operations

System Solution

System Solution

System Solution

3 System of Equations

System Operations

System Solution

System Solution