Linear Algebra
Optimization
Differential Equations

## 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,

```
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