Gaussian Elimination

In linear algebra, Gaussian elimination is an algorithm for solving systems of linear equations. It can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix. The method is named after Carl Friedrich Gauss, but it was not invented by him.

Elementary row operations are used to reduce a matrix to what is called triangular form (in numerical analysis) or row echelon form (in abstract algebra). Gauss–Jordan elimination, an extension of this algorithm, reduces the matrix further to diagonal form, which is also known as reduced row echelon form. Gaussian elimination alone is sufficient for solving systems of linear equations in many applications, and requires fewer calculations than the Gauss–Jordan version.