﻿ Matrix.Solve Method (Double[,], Double[,], Boolean)

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Returns the solution matrix if the matrix is square or the least squares solution otherwise.

Namespace:  Accord.Math
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.8.0
Syntax
```public static double[,] Solve(
this double[,] matrix,
double[,] rightSide,
bool leastSquares = false
)```

#### Parameters

matrix
Type: SystemDouble
The matrix for the linear problem.
rightSide
Type: SystemDouble
The right side b.
leastSquares (Optional)
Type: SystemBoolean
True to produce a solution even if the matrix is singular; false otherwise. Default is false.

Type: Double

#### Usage Note

In Visual Basic and C#, you can call this method as an instance method on any object of type . When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).
Remarks
Please note that this does not check if the matrix is non-singular before attempting to solve. If a least squares solution is desired in case the matrix is singular, pass true to the leastSquares parameter when calling this function.
Examples
```// Create a matrix. Please note that this matrix
// is singular (i.e. not invertible), so only a
// least squares solution would be feasible here.

Double[,] matrix =
{
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 },
};

// Define a right side matrix b:
Double[,] rightSide = { {1}, {2}, {3} };

// Solve the linear system Ax = b by finding x:
Double[,] x = Matrix.Solve(matrix, rightSide, leastSquares: true);

// The answer should be { {-1/18}, {2/18}, {5/18} }.```
See Also