Cramer's Rule is a mathematical theorem used to solve a system of linear equations with as many equations as unknowns, provided the determinant of the coefficient matrix is non-zero. It expresses each variable as a quotient of determinants, making it computationally expensive for large systems but straightforward for small ones.

Cramer's Rule

A mathematical theorem is a statement that has been proven to be true based on previously established statements and axioms. Theorems are fundamental in mathematics as they provide a framework for understanding and advancing mathematical knowledge through logical reasoning.

mathematical theorem

A system of linear equations is a collection of two or more linear equations involving the same set of variables, where the solution is the set of values that satisfy all equations simultaneously. Solving these systems can be done through various methods such as graphing, substitution, elimination, or using matrices and determinants for more complex systems.

system of linear equations

determinant of the coefficient matrix

Non-zero Determinant

each variable as a quotient of determinants

computationally expensive

large systems

Small systems refer to simplified models or frameworks that capture the essential dynamics of a larger, more complex system. They are used to study and understand the fundamental behaviors and interactions within a system without the computational or analytical complexity of a full-scale model.

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