example of Cramer’s rule

Say we want to solve the system

3x+2y+z-2w = 4
2x-y+2z-5w = 15
4x+2y-5w = 1
3x-2z-4w = 1.

The associated matrix is


whose determinantMathworldPlanetmath is Δ=-65. Since the determinant is non-zero, we can use Cramer’s rule. To obtain the value of the k-th variable, we replace the k-th column of the matrix above by the column vectorMathworldPlanetmath


the determinant of the obtained matrix is divided by Δ and the resulting value is the wanted solution.


Title example of Cramer’s rule
Canonical name ExampleOfCramersRule
Date of creation 2013-03-22 12:50:33
Last modified on 2013-03-22 12:50:33
Owner drini (3)
Last modified by drini (3)
Numerical id 7
Author drini (3)
Entry type Example
Classification msc 15A15