2022•Unpublished venueRequires access

Linear systems

André Lukas

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Abstract

Abstract Abstract linear systems as well as systems of linear equations are introduced. It is shown that the general solution to an inhomogeneous system is given by a special solution to the inhomogeneous system plus the general solution to the associated homogeneous system. An algorithm to solve systems of linear equations in terms of row operations is formulated. The results are applied to the geometry of affine lines, planes and their higher-dimensional analogues.

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Abstract Abstract linear systems as well as systems of linear equations are introduced. It is shown that the general solution to an inhomogeneous system is given by a special solution to the inhomogeneous system plus the general solution to the associated homogeneous system. An algorithm to solve systems of linear equations in terms of row operations is formulated. The results are applied to the geometry of affine lines, planes and their higher-dimensional analogues.

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Available abstract

Abstract Abstract linear systems as well as systems of linear equations are introduced. It is shown that the general solution to an inhomogeneous system is given by a special solution to the inhomogeneous system plus the general solution to the associated homogeneous system. An algorithm to solve systems of linear equations in terms of row operations is formulated. The results are applied to the geometry of affine lines, planes and their higher-dimensional analogues.

Key concepts: System of linear equations, Linear system, Affine transformation, Homogeneous, Mathematics, Linear equation, Applied mathematics, Mathematical analysis

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