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Gaussian elimination
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Gaussian elimination is a step-by-step method for solving systems of linear equations by manipulating the equations to make them simpler and easier to solve. It matters because it's one of the most fundamental and widely-used techniques in mathematics and engineering for finding solutions to practical problems involving multiple equations and unknown values.
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Animation of Gaussian elimination. Red row eliminates the following rows, green rows change their order. In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of an invertible matrix. The method is named after Carl Friedrich Gauss (1777–1855).
To perform row reduction on a matrix, one uses a sequence of elementary row operations to modify the matrix until the lower left-hand corner of the matrix is filled with zeros, as much as possible. There are three types of elementary row operations: