We will study the row space of a matrix. The row space of an n × m matrix A is defined a...

We will study the row space of a matrix. The row space of an n × m matrix A is defined as the span of the row vectors of A (i.e., the set of their linear combinations). For example, the row space of the matrix

is the set of all row vectors of the form

Consider an n × m matrix E in reduced row-echelon form. Using your work in Exercise 71 as a guide, explain how you can find a basis of the row space of E. What is the relationship between the dimension of the row space and the rank of E?