Gaussian elimination

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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 matrixto transform it to echelon 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(If a11=0, it is necessary to interchange two rows first.) The first row now remains untouched and the process is repeated with the remaining rows, dividing the second row by a22 to produce a 1, and subtracting suitable multiples of the new second row from the subsequent rows to produce zeros below that 1. The method continues in the same way. The essential point is that the corresponding set of equations at any stage has the same solution set as the original. (See also simultaneous linear equations.)

Subjects: Mathematics.

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