iosr-JCE  Volume-28 ~ Issue-4 ~ Jul. - Aug. 2026

Abstract: This work algebraically demonstrates the equivalence between Cramer's rule and the Gauss-Jordan method for solving 2x2 systems of linear equations. Through matrix and symbolic development, it is shown that both procedures lead to algebraically equivalent expressions when the system has a unique solution. A comparative analysis.....

Key Word: Gabriel Cramer's rule, Gauss-Jordan, equivalence, algebraics, linear algebra, system of linear equations, computational complexity.

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[2]. Babajee, D. K. R. (2013). A Comparison Between Cramer's Rule And A Proposed 2 × 2 Cramer-Elimination Method To Solve Systems Of Three Or More Linear Equations. Scientific & Academic Research Council, ANPRAS (Allied Network For Policy, Research And Actions For Sustainability). Https://Www.Researchgate.Net/Publication/255981900
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[5]. Higham, N. J., & Mary, T. (2022). Solving Block Low-Rank Linear Systems By LU Factorization Is Numerically Stable. IMA Journal Of Numerical Analysis, 42(2), 951–980. Https://Doi.Org/10.1093/Imanum/Drab020.

Abstract: Diabetes mellitus is still one of the most common chronic diseases worldwide and associated with high rates of hospital readmission and increased costs of health care. Early prediction of diabetes risk and re-admission to the hospital can greatly enhance patient management and reduce the load on health systems. Recent advances in artificial intelligence have produced predictive models can analyse complex health care data. We propose a hybrid deep learning framework that combines Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM....

Key Word: Hybrid Deep Learning; CNN–LSTM; Diabetes Prediction; Hospital Readmission; Multimodal Healthcare Data; Predictive Healthcare Analytics.

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