Linear Representation of Vector Group, Quick Solutions to Maximal Independent Group and Linear Equations in Linear Algebra

Through improving the process of "the linear representation of vector and vector group, and seeking solution to the maximal independent subset of vector group and linear equations" in linear algebra, this article simplifies the conventional two-step solution into one-step. The traditional two steps are: first, the matrix consisting of column vectors or the augmented matrix of linear equations is transformed into a ladder by the means of elementary row transformation; then this ladder matrix is transformed into a simplified row ladder matrix by doing one more elementary row transformation. However, with the improved method, we can work out solutions in one single step of elementary row transformation by transforming the transpose matrix of column vectors or the transpose augmented matrix of linear equations into a ladder matrix. The new method, thus, not only reduces half of the workload but also the difficulty of problem solving.