Mathematics · important
Cramer's rule for three variables for JEE
Test of consistency and solution of simultaneous linear equations in two or three variables using matrices
Formula
For \(AX=B\), if \(D=\det(A)\ne 0\), then \(x=\dfrac{D_x}{D},\ y=\dfrac{D_y}{D},\ z=\dfrac{D_z}{D}\), where \(D_x,D_y,D_z\) are obtained by replacing the corresponding coefficient columns of \(A\) by the constants column.
Variables: \(D\): determinant of coefficient matrix.
Conditions: Applicable to a square system with \(D\ne 0\).
Direct solution of 3-variable linear equations.