Cramer’s Rule

Cramer’s Rule

A method for solving a linear system of equations using determinants. Cramer’s rule may only be used when the system is square and the coefficient matrix is invertible.

System of three linear equations: x − y + z = 10, x + 2y + 3z = 22, 4x + 5y + 6z = 12
Cramer's Rule solution showing x=−31/12, y=−29/6, z=31/4, each as a ratio of 3×3 determinants with values 10,−1,1,11,2,3,12,5,6.

See also

Cofactors, expansion by cofactors