ABSTRACT
This chapter deals with some further properties of matrices and with certain further operations which can be carried out on matrices. It shows that social scientists can find a single premultiplying matrix which corresponds to a sequence of two elementary row operations. However, it is often convenient to think of a sequence of elementary row operations as being represented by a similar sequence of premultiplying matrices, each of which corresponds to one elementary row operation and which hence may be called an elementary matrix. It is interesting to consider these elementary operations and the derivation of an echelon matrix in the light of the discussion of linear combinations and linear dependence of vectors. The rank of a rectangular matrix is defined as the maximum number of linearly independent rows in the matrix. In order to show one reason for an interest in elementary operations, consider for a moment the problem of solving a set of linear equations.
