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Linear Algebra, as part of Algebraic Geometry in Mathematics, studies the properties and structures of vector spaces and linear mappings between them. It forms the foundation for various mathematical disciplines and applications in science and engineering. Through the use of matrices and tensors, it provides a systematic way to manipulate and solve systems of linear equations, enabling analysis and understanding of phenomena involving multiple variables and dependencies. The concepts and techniques developed in Linear Algebra have far-reaching implications in areas such as differential equations, optimization, cryptography, and machine learning.