In this paper, for the prediction of Alzheimer’s disease (AD), linear algebra empowers a state-of-the-art machine learning algorithm. Based on a large dataset (El Kharoua (2024), 10.34740/kaggle/dsv/8668279) of 2149 patients with fully recorded medical history, our ensemble model customizes complex machine learning models such as neural networks and XGBoost classifiers that show improvements with promising accuracy (95.35%) and AUC-ROC (0.99) compared to the state-of-the-art method. To improve neural networks, this research aims to use linear algebra-based data preprocessing and feature engineering. This can help understand the practicability of these methods in medical diagnostics and our research shows significant improvements proving so. The research is adding to a larger field of studies suggesting that noninvasive, inexpensive early AD detection and prognosis could soon become valuable in clinical settings.