GAUSSIAN ELIMINATION

 It is usually understood as a sequence of operations performed on the corresponding matrix of coefficients. This method 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.

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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:

• Swapping two rows,

• Multiplying a row by a nonzero number,

• Adding a multiple of one row to another row.

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For example, in the following sequence of row operations, the third and fourth matrices are the ones in row echelon form, and the final matrix is the unique reduced row echelon form.

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