<![CDATA[This study was motivated by the limited empirical evidence on the application of systematic methods in solving linear equation systems in physics education, particularly in dynamic electricity, to support students' mathematical reasoning abilities and learning outcomes. Previous studies have mostly emphasized conceptual understanding, while the use of the Gauss–Jordan method as a structured problem-solving approach has received limited attention. Therefore, this study aims to analyze the impact of applying the Gauss–Jordan method on students' mathematical reasoning abilities and learning outcomes. This study used a quasi-experimental design with a posttest-only control group. Participants consisted of 67 high school students and 65 physics education students selected through purposive sampling. Data were collected using essay tests based on four indicators of mathematical reasoning and student response questionnaires. Data were analyzed using the Shapiro–Wilk test, independent samples t-test, and Mann–Whitney U test. The results showed that students in the experimental group obtained significantly higher scores in mathematical reasoning and learning outcomes compared to students in the control group (p < 0.05). The novelty of this study lies in the integration of algorithm-based and matrix-oriented problem solving in dynamic electricity learning. These findings indicate that systematic mathematical modeling strengthens students' reasoning and conceptual understanding in physics. However, the limited sample size restricts generalization, and further research is recommended.]]>
