Mathematics · essential
Consistency criterion for three variables via determinant for JEE
Test of consistency and solution of simultaneous linear equations in two or three variables using matrices
Formula
For a 3-variable system \(AX=B\): unique solution if \(\det(A)\ne 0\); if \(\det(A)=0\), then the system may be either inconsistent or have infinitely many solutions.
Variables: \(A\): coefficient matrix.
Conditions: For square systems of order 3.
Quick test before applying inverse/Cramer method.