Linear Equation of upto 10 variables -- Solution

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Gauss's Method

 A1 X1 + A2 X2 + A3 X3 + A4 X4 + A5 X5 + A6 X6 + A7 X7 + A8 X8 + A9 X9 + A10 X10 = B1 + + + + + + + + + =

 x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x1 = x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x2 = x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x3 = x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x4 = x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x5 = x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x6 = x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x7 = x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x8 = x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x9 = x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x10 =

Number of variables -->

 x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 =

 x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 =

 x4 + x5 + x6 + x7 + x8 + x9 + x10 = x4 + x5 + x6 + x7 + x8 + x9 + x10 = x4 + x5 + x6 + x7 + x8 + x9 + x10 = x4 + x5 + x6 + x7 + x8 + x9 + x10 = x4 + x5 + x6 + x7 + x8 + x9 + x10 = x4 + x5 + x6 + x7 + x8 + x9 + x10 = x4 + x5 + x6 + x7 + x8 + x9 + x10 =

 x5 + x6 + x7 + x8 + x9 + x10 = x5 + x6 + x7 + x8 + x9 + x10 = x5 + x6 + x7 + x8 + x9 + x10 = x5 + x6 + x7 + x8 + x9 + x10 = x5 + x6 + x7 + x8 + x9 + x10 = x5 + x6 + x7 + x8 + x9 + x10 =

 x6 + x7 + x8 + x9 + x10 = x6 + x7 + x8 + x9 + x10 = x6 + x7 + x8 + x9 + x10 = x6 + x7 + x8 + x9 + x10 = x6 + x7 + x8 + x9 + x10 =

 x7 + x8 + x9 + x10 = x7 + x8 + x9 + x10 = x7 + x8 + x9 + x10 = x7 + x8 + x9 + x10 =

 x8 + x9 + x10 = x8 + x9 + x10 = x8 + x9 + x10 =

 x9 + x10 = x9 + x10 =

 x10 =

 * In Gauss method, the solution is exact and the precondition is that the leading elements (yellow cells) should not be zero. Here in each successive table, the no. of variables is reduced by one through successive elimination of one variable This is called Direct Procedure.. The computation starts from the last variable upwards  which is called Reverse Procedure. * We have programmed to overcome the bottleneck if leading element is zero. * The number N of arithmetic operations necessary to realize the Gaussian method is determined by the formula N = (2n(n+1)(n+2)/3) + n(n-1) where n is the number of unknowns or approximately N is proportional to n3