Abstract: In this paper, the two-step solution process is simplified to the one-step process, in which the transpose matrix of column vectors or the transpose augmented matrix of linear equations are transformed into a ladder by the means of elementary row transformation. The improvement not only reduces a certain amount of the workload but also lowers the difficulty of seeking solutions.

Key words: Vector group, Maximal independent group, Linear equations, Matrix, Transpose, Elementary row transformation, Ladder-shaped matrix, Simplified row ladder matrix