Study on the problem of linear equations A_(mn)X_(n1)=B_(m1)

The method of elementary transformation is often used in solving linear equations.If the matrix of coefficient is an invertible matrix,the inverse of matrix to solve the linear equations is used.This paper demonstrates a new method of solving linear equations—using the theory of the generalized matrix to solve linear equations.Firstly,it presents the definitions of the full rank matrix and weak inverse of matrix,and then it comes to conclusion that any one m×n matrix must have an non-unique weak inverse of matrix by means of using the necessary and sufficient condition that a matrix is the weak inverse of another matrix,finally,it gives the solving method of a weak inverse of matrix and a new method of solving linear equations by the matrix.