Cramer's law
- In linear algebra, Cramer's law is a direct method of solving a system of linear equations.
- This method expresses the determinant of the coefficient matrix and the coefficient of a transformed form of the multiplier matrix.
- This method is valid only if a unique solution of the system is possible.
- This law is named after Gabriel Cramer (1704-1752) who propounded it in 1750.
Let the rule be to solve for Ax = b
where,
A is the coefficient matrix of the system
x = ( 21 , ... , m ) is the column vector of all the unknown quantities in the system, and b is the non-variable terms of the system.
According to Cramer's law, is the column vector the value of unknown quantities can be obtained by the following formula.
where,
A is the matrix obtained by substituting the column vector b in the j-th column of the coefficient matrix A. Formula for two and three variables 2 Let the system of two linear equations with unknown quantities be two linear equations with two unknown quantities.
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