<![CDATA[Competency-based assessment systems are increasingly important in education and industry to objectively assess individual abilities, overcoming the subjectivity issues inherent in traditional assessment methods. This study aims to develop an innovative competency assessment system by combining Assessment Matrix and Linear Algebra, specifically using the Analytic Hierarchy Process (AHP) method to systematically and accurately determine the weight of criteria. The research data were taken from a dataset of college students, with five main criteria of competence, including technical skills, cooperation, and creativity. The data normalization process was carried out using Min-Max Scaling and Z-Score Normalization to ensure consistency, followed by the construction of an AHP comparison matrix based on the level of importance between criteria. The weight of the criteria was calculated using the eigenvector method, and the consistency test was carried out through the Consistency Ratio (CR) to ensure the validity of the matrix (CR < 0.1). The final assessment was obtained by multiplying the AHP weights by the student's scores for each criterion. The results showed that this approach resulted in a more objective, transparent, and accurate assessment system than conventional methods, with the potential to improve fairness in evaluation in the academic environment. This research provides a new contribution in the application of linear algebra to the development of competency assessment systems, as well as offering practical solutions for educators and human resource managers in improving performance evaluation.]]>
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