Linear Algebra

Cramer's Rule is a fundamental algorithm in linear algebra

Cramer’s Rule is a fundamental algorithm in linear algebra designed specifically to find the unique solution of a system of linear equations. It leverages the concept of determinants to solve for each variable individually. The material is presented clearly, drawing on the provided sources, including specific examples for $2 \times 2$ and $3 \times 3$ systems. 1. Explanation of Cramer’s Rule Cramer’s Rule can only be applied to a system of linear equations that has a unique solution. For this rule to be applicable, two critical conditions regarding the matrix representation $Ax=b$ must be met: