Solution of system of equations using Cramer method

Let the system (2.1) consist of linear equations with unknown quantities and its determinant then unknown quantities can be found accordingly to the formulas by Cramer:

, ,

where is the determinant of the system; is determinant obtained from the determinant of the system by substituting the column by the matrix-column :

.

For example, consider the system (2.1) which consists of 3 linear equations with 3 unknowns . Then unknowns can be found accordingly to the formulas by Cramer:

, , ,

where , , , .

Let’s illustrate this method by example.

Example 1. Solve the given system of equations using Cramer method:

.

Solution. Find the determinant of the given system:

.

Its determinant is non-zero. Apply the formulas by Cramer:

, ,

, ,

, .

Checking by substitution into the initial system:

.

Дата добавления: 2014-01-11