System of Linear Equations.

The LinearEquations class computes the solution to a real system of linear equations (general, band and tridiagonal matrices): A * X = B.

 In this example the LinearEquations class is used to solve:

            2*x1 + 5*x2 + 3*x3 = 5;
            1*x1 + 5*x2 + 7*x3 = 3;
            8*x1 + 2*x2 + 3*x3 = 8;

C# Code

using DotNumerics.LinearAlgebra;

using DotNumerics;

public void LinearAlgebraSolve()

{

    //using DotNumerics.LinearAlgebra;

    //using DotNumerics;

    Matrix A = new Matrix(3, 3);

    A[0, 0] = 2; A[0, 1] = 5; A[0, 2] = 3;

    A[1, 0] = 1; A[1, 1] = 5; A[1, 2] = 7;

    A[2, 0] = 8; A[2, 1] = 2; A[2, 2] = 3;

    Matrix B = new Matrix(3, 1);

    B[0, 0] = 5;

    B[1, 0] = 3;

    B[2, 0] = 8;

    LinearEquations leq = new LinearEquations();

    Matrix X = leq.Solve(A, B);

    Matrix AXmB = A * X - B;

}

Solution

A=
2.000, 5.000, 3.000, 
1.000, 5.000, 7.000, 
8.000, 2.000, 3.000, 

B=
5.000, 
3.000, 
8.000, 

X=
0.902, 
0.804, 
-0.275, 

AXmB(A*X-B) =
0.000, 
0.000, 
0.000,