Let us considér a system óf n linear équations with n variabIes a11x1a12x2.a1nxnb1 a21x1a22x2.a2nxnb2 an1x1an2x2.annxnbn Assume that the diagonal coefficients a ii, i 1, 2,, n are diagonally dominant.If this is not the case then the above system of equations are rearranged in such a way that the above condition holds.Substituting these values to the above system and get the first approximate value of x 1, denoted by x 1 (1).Now, substituting x 1 (1) for x1 and x 3 (0), x 4 (0),, x n (0) for x 3, x 4,, x n respectively and we find x 2 (1) from second equation of the above system of equations, the first approximate value of x 2.
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