Linear Equation System Solver

This application calculates $X$ from the matrix equation \[ AX = B \] where $A$ is a $m\times m$ real or complex matrix, $X$ and $B$ are $m\times n$ real or complex matrices. For example, the system of linear equations \begin{eqnarray*} x_1 - 2x_2 + 3x_3 &=& 9 \\ 5x_1 + 8x_2 - x_3 &=& -5\\ 2x_1 + x_2 + x_3 &=& 3 \end{eqnarray*} can be written in the form of matrix equation \[ \left[\begin{array}{rrr} 1 & -2 & 3 \\ 5 & 8 & -1 \\ 2 & 1 & 1 \end{array}\right] \left[ \begin{array}{c} x_1 \\ x_2 \\ x_3 \end{array} \right] = \left[ \begin{array}{r} 9 \\ -5 \\ 3 \end{array} \right] \] with $m=3$ and $n=1$. In the special case that $B=I$ we obtain $X=A^{-1}$, i.e. the inverse matrix of $A$.

See Input Data for the description of how to enter matrix or just click Example for a simple example.

Linear Equation Calculator

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