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Linear subspaces with shading

A line and two planes passing through the origin (making them vector subspaces in the three-dimensional vector space R3.

Linear algebra is a branch of algebra dealing with the study of vector spaces and the linear transformations inter them. In a more abstract set up linear algebra is the category of vector spaces.

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Concepts in linear algebra are central in many areas of mathematics, both pure and applied. The precepts of linear algebra form the basis of abstract algebra, and are heavily used in vector calculus, differential equations, analytic geometry, physics, computer science, economics, and engineering.