Cramer's Rule is a mathematical theorem used to solve systems of linear equations with as many equations as unknowns, utilizing determinants. It provides an explicit formula for the solution of the system.
5 Must Know Facts For Your Next Test
Cramer's Rule can only be applied to square matrices where the number of equations equals the number of unknowns.
The rule involves calculating determinants of the coefficient matrix and matrices formed by replacing one column with the constants from the equations.
If the determinant of the coefficient matrix is zero, Cramer's Rule cannot be applied because it indicates that there is either no unique solution or infinitely many solutions.
For a system of $n$ linear equations, $n+1$ determinants need to be calculated: one for the coefficient matrix and one for each variable's matrix.
Cramer's Rule is computationally expensive for large systems due to determinant calculation complexity.