Answer: In Exercises 69 through 72, we will study the row space of a matrix. The row

Chapter 3, Problem 71

(choose chapter or problem)

In Exercises 69 through 72, we will study the row space of a matrix. The row space of an n x 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 1 2 3 4" 1 1 1 1 L2 2 2 3j it is the set of all row vectors of the form a [l 2 3 4 ] + * [ l 1 1 l] + c [2 2 2 3] Consider an arbitrary n x m matrix A. a. What is the relationship between the row spaces of A and E = rref(A)? {Hint: Examine how the row space is affected by elementary row operations.) What is the relationship between the dimension of the row space of A and the rank of A?