# A Nonstandard Approach to Cramer's Rule

by Sidney H. Kung

This article originally appeared in:
College Mathematics Journal
January, 1988

Subject classification(s): Algebra and Number Theory | Linear Algebra
Applicable Course(s): 3.8 Linear/Matrix Algebra

Cramer's Rule gives an explicit formulation for the unique solution to a system of $n$ equations in $n$ unknowns when the coefficient matrix of the system is invertible.  The standard proof is developed using the adjoint matrix.  In this capsule, the author uses properties of determinants and general matrix algebra to provide an alternative proof of Cramer's Rule.

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Capsule Course Topic(s):
Linear Algebra | Determinants
Linear Algebra | Matrix Algebra
Linear Algebra | Solving Linear Systems: Algebraic