Chapter 1.1, Problem 23E

In Exercises 23 and 24, key statements from this section are either quoted directly, restated slightly (but still true), or altered in some way that makes them false in some cases. Mark each statement True or False, and justify your answer. (If true, give the approximate location where a similar statement appears, or refer to a definition or theorem. If false, give the location of a statement that has been quoted or used incorrectly, or cite an example that shows die statement is not true in all cases.) Similar true/false questions will appear in many sections of die text.

23.

1. a. Every elementary row operation is reversible.
2. b. A 5 × 6 matrix has six rows.
3. c. The solution set of a linear system involving variables x₁, …, x_n is a list of numbers (s₁, …, s_n) that makes each equation in the system a true statement when the values s₁, …, s_n are substituted for x₁, …, x_n respectively.
4. d. Two fundamental questions about a linear system involve existence and uniqueness.