Abstract: The rank of matrix is an important concept in linear algebra. In this paper, different from the traditional teaching design of the definition of matrix rank, we start with the problem of whether the standard form of matrix is unique or not, and then transform the problem into the problem of whether the primary transformation changes the highest order of the non-zero sub formula of matrix. Through analysis, we get that the highest order of the non-zero sub formula is the invariant in the process of the primary transformation, thus leading to the concept of matrix rank. Such new approach is not only very natural in introducing, but also enables students to recognize the meaning of the definition of the rank of matrix. Therefore, students can understand this abstract concept more easily and improve the teaching effect.

Key words: The rank of matrix, Elementary transformation, Canonical form of matrix, The teaching design