Cramerszabály

Cramerszabály is a mathematical rule used in algebra, system of equations, and linear algebra to determine the value of a variable when some but not all values of other variables are known. It is named after the Danish mathematician Gabriel Cramer.

The rule states that if a system of linear equations has a solution, it can be found by applying Cramerszabály to the matrix of coefficients and the variable in question. To apply the rule, one forms a new determinant called the cofactor determinant, which is calculated by taking the original determinant of the coefficient matrix and replacing the column or row related to the variable in question with the variable's own coefficients, while all other entries in the column or row remain unchanged.

The value of the variable is then the quotient of the cofactor determinant and the determinant of the coefficient matrix. In algebraic manipulation, this rule is useful for finding the value of one unknown variable in a system of linear equations.

In practice, Cramerszabály is often used as an alternative to Gaussian elimination or matrix inversion when solving systems of linear equations with known coefficients and unknown variables. The method also facilitates the derivation of inverse matrix formula.