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[[[>50 Borrowing text from https://en.wikipedia.org/wiki/Linear_algebra ]]] Linear algebra is the study of vector spaces and linear mappings or linear functions between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces. Both pure and applied mathematics use results from linear algebra. Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science (including machine learning), computer animation, and the social sciences (particularly in economics). Because linear algebra is such a well-developed theory, non-linear mathematical models are sometimes approximated by linear models.