Applied Mathematics · Ch 2 — Algebra

Cramer's Rule

2.8.2

Cramer's Rule

Cramer's rule solves a system of linear equations $AX = B$ using only determinants, without ever explicitly computing an inverse. For a system in two variables $a_1x + b_1y = c_1$ , $a_2x + b_2y = c_2$ , let $D$ be the determinant of the coefficient matrix, and let $D_x$ , $D_y$ be the determinants obtained by replacing the $x$ -column or the $y$ -column of that matrix with the constants column:

x = \dfrac{D_x}{D}, \qquad y = \dfrac{D_y}{D}, \qquad \text{provided } D \neq 0

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← Previous · 2.8.1Example 39 — Solve the following system of equation using matrix method: x + y + z …Next · 2.8.2 →Example 40 — Solve the following system of equation using Cramer's rule: 2x - 3y = …