Gaussian Elimination

Gaussian Elimination is the name given to a particular systematic procedure for solving a set of linear equations in several unknowns. This is normally carried out by applying elementary row operations to the augmented matrix.
example of an augmented matrix

To transform it to (row-)echlon form. The method is to divide the first row by a₁₁, and then subtract suitable multiples of the first row from the subsequent rows, to obtain a matrix of the form:
example of a matrix in echlon form

(If a₁₁ = 0, it is necessary to interchange two rows first.) The first row now remains untouched and th eprocess is the second row by a'₂₂ to produce a new 2nd row from the subsequent rows to produce zeros below that 1. The method continues the same way. The essential point is that the corresponding set of equations at any stage has the same solution set as teh original.

For further reading or for the extension, go onto Gauss-Jordan Elimination

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