General Solutions of Consistent and Inconsistent Linear Equation Systems Via Maple

Abstract

This paper furnishes a general solution about the linear equation system $\boldsymbol{Ax}=\boldsymbol{g}$. The analytic solutions to the problem of finding the vector $\boldsymbol{x}$, from among the general solution set of the system if it is consistent, and from among the least squares solution set of the system if it is inconsistent, such that the norm of $\boldsymbol{x}-\boldsymbol{x}_{\mathbf{0}}$ is minimum for a given vector $\boldsymbol{x}_{\mathbf{0}}$ are established. For inverse matrix of A, it is used generalized inverse (Moore-Penrose inverse) by using algorithm and Maple. Analytic results, we obtained are satisfied by using algorithm with numerical examples.