利用初等列变换解线性方程组

his paper gives and proofs a theorem, for any matrix A, do elementary column operations, change it to a matrix which is partitioned to two submatrices which left one is column full rank and right one is zero matrix. Then do same elementary column operations to a unit matrix with same column number as A, and do same partition to the result, then right submatrix of it, is just basic solution set of homogeneous linear equations AX=O. On the basis of the theorem, lots of proplems of linear algebra can be resolved and lots of theorems can be proofed by elementary column operations. So any techniques of elementary row operations on basis of Gauss elimination method can be discarded. The paper will reveal that them will not easy to learn and to program and to proof something as techniques giving by the paper. In future, the students to learn linear algebra can completely have not the concepts like Gauss elimination method, free argument, first argument, reduced row echelon form, etc.