Excuse me, teacher, why is "the rank of a matrix equal to the rank of its column vector group, and also equal to the rank of its row vector group"? How to understand the relationship between the rank of matrix and the rank of vector group, please click in detail

Excuse me, teacher, why is "the rank of a matrix equal to the rank of its column vector group, and also equal to the rank of its row vector group"? How to understand the relationship between the rank of matrix and the rank of vector group, please click in detail

First of all, in order to help you understand, you need to clarify two definitions: the definition of the rank of the matrix: there is a k-order subformula is not 0, for any K + 1-order subformula is 0, then K is the rank of the matrix. The definition of the rank of the vector group: the number of vectors contained in the maximal linearly independent group of the vector group