<![CDATA[Determinants are conventionally defined only for square matrices, which leaves the theoretical discussion of rectangular matrices relatively undeveloped. This study aims to extend determinant theory by introducing a generalized form of the cofactor expansion applicable to non-square matrices. The method employed in this research is a theoretical–analytical approach that begins with identifying fundamental determinant axioms and proceeds with the construction of a recursive cofactor expansion for matrices with . Worked examples are used to demonstrate the linearity, antisymmetry under row interchange, and reduction consistency of the proposed formulation when applied to square matrices. The findings indicate that the generalized expansion preserves essential algebraic properties and shows compatibility with established rectangular determinant definitions, including the Radić determinant. Overall, this study provides a coherent theoretical foundation for the generalized determinant of rectangular matrices and contributes to broader applications of determinant-based analysis in linear algebra]]>
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