This is to be a C++ program I repeat C++ not C# make sure it compiles error free in Visual Studio 2015: use the following steps and algorithm for Gaussian Elimination with Backward Substitution to solve the n n linear system

E1 : a11x1 + a12x2 + +a1nxn = a1,n+1

E2 : a21x1 + a22x2 + +a2nxn = a2,n+1

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En : an1x1 + an2x2 + +annxn = an,n+1

INPUT: number of unknowns and equations n; augmented matrix A = [ai j], where 1

i n and 1 j n + 1.

OUTPUT: solution x1, x2, . . . , xn or message that the linear system has no unique solution.

Step 1: For i = 1, . . . , n 1 do Steps 24. (Elimination process.)

Step 2: Let p be the smallest integer with i p n and api _= 0.

If no integer p can be found

then OUTPUT (no unique solution exists);

STOP.

Step 3: If p _= i then perform (Ep) (Ei).

Step 4: For j = i + 1, . . . , n do Steps 5 and 6.

Step 5: Set mji = aji/aii.

Step 6 : Perform (Ej mjiEi) (Ej);