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Linear Algebra, as part of Analytic Number Theory in Mathematics, focuses on the study of linear equations and their properties. It involves vectors, matrices, and transformations, providing a foundation for understanding complex systems in Science. The subject explores concepts such as determinants, eigenvalues, and orthogonality, which are essential in various scientific fields like physics, computer science, and engineering. In the context of Analytic Number Theory, Linear Algebra finds applications in studying Diophantine equations and analyzing lattice point problems, contributing significantly to the broader field of Mathematics.