The evaluation of matrix rank based on determinant-operation

The general method of evaluating matrix rank from the present teaching materials Advanced Algebra is that by using the method of elementary-transformation of row, the matrix is changed into its equivalent ladder-shaped matrix, whose number of non-zero row is the rank of the matrix. The method is concise, but it is difficult to be put into practice. The study introduces a new method of evaluating matrix rank based on the determinant-operation. The method is not only easy to understand but also convenient to master.