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Solve Simultaneous Equation

Calculate the solution vector (A) for the linear simultaneous equations, from the linear equation matrix (M), and the result vector (C).

The simultaneous equations are solved using the Crout or Chelensky factorial

`L · U = M `
`M · A = C `
`L · D = C `
`U · A = D `

where :

L is a lower diagonal matrix
U is an upper diagonal matrix.
D is an intermediate result vector

Enter each matrix row as a comma separated list, with a new line for each row. Matrices must have an equal number of elements in each row. The number of rows in the matrix must be equal to the number of columns. The matrix equations must be independent (ie well conditioned - determinant not equal to zero). If the matrix determinant equals zero, the equations are indeterminant. Enter vectors as a comma separated list. The number of elements in the vector must equal the number of matrix columns.

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Links : ±
CALCULATOR : Matrix And Vector Solve (Simultaneous Equation Solution) [FREE]   ±

Calculate the matrix and vector dot product solution (simultaneous equation solution) for a square n x n matrix and vector.

The solution can be calculated for either the matrix or the transpose of the matrix. The number of matrix columns must be equal to the number of matrix rows. The check vector should be equal to the input vector. The matrix values must be independent for a solution (the matrix determinant must be non zero).

Tool Input

  • rndtype : Rounding Type For Small Values
  • matype : Matrix Operation Type
  • M : Simultaneous Equation Input Matrix

Tool Output

  • |M| : Check Determinant (!= 0)

CALCULATOR : Matrix And Vector Solve (Simultaneous Equation Solution - File Data - Modern Browser Required) [FREE]   ±

Calculate the matrix and vector dot product solution (simultaneous equation solution) for a square n x n matrix and vector from file data.

The solution can be calculated for either the matrix or the transpose of the matrix. The number of matrix columns must be equal to the number of matrix rows. The check vector should be equal to the input vector. The matrix values must be independent for a solution (the matrix determinant must be non zero).

Save the matrix to a text file as tab or comma separated rows with each row on a new line (or copy and past cells from a spreadsheet). The vector can be defined either in the text file or on the calculation page. As an option, save the vector as a comma or tab separated list. Refer to the example text file in resources.

Tool Input

  • rndtype : Rounding Type For Small Values
  • matype : Matrix Operation Type
  • M : Simultaneous Equation Input Matrix

Tool Output

  • |M| : Check Determinant (!= 0)