Cramer's Rule

Solves square linear systems with determinants.

x_{i} = \frac{det ( A _{i} )}{det ( A )}

Variables

Works only when $det A \neq = 0$ . Practical for 2×2 and 3×3 systems; elimination is faster for larger ones.

$2 x + 3 y = 12, x - y = 1$ : $D = - 5$ , $x = \frac{- 15}{- 5} = 3$ , $y = 2$ .

Solve systems of 2 or 3 linear (or nonlinear) equations with Gaussian elimination, substitution and Cramer's rule.

Determinant of a Matrix

Scalar that tells whether a matrix is invertible.