23. a. True. See the remarks following the box titled Elementary Row Operations.
b. False. A 5 × 6 matrix has five rows.
c. False. The description given applied to a single solution. The solution set consists of all possible
solutions. Only in special cases does the solution set consist of exactly one solution. Mark a statement
True only if the statement is always true.
d. True. See the box before Example 2.
24. a. True. See the box preceding the subsection titled Existence and Uniqueness Questions.
b. False. The definition of row equivalent requires that there exist a sequence of row operations that
transforms one matrix into the other.
c. False. By definition, an inconsistent system has no solution.
d. True. This definition of equivalent systems is in the second paragraph after equation (2).
22. a. False. See the statement preceding Theorem 1. Only the reduced echelon form is unique.
b. False. See the beginning of the subsection Pivot Positions. The pivot positions in a matrix are
determined completely by the positions of the leading entries in the nonzero rows of any echelon
form obtained from the matrix.
c. True. See the paragraph after Example 3.
d. False. The existence of at least one solution is not related to the presence or absence of free variables.
If the system is inconsistent, the solution set is empty. See the solution of Practice Problem 2.
e. True. See the paragraph just before Example 4.
23. Yes. The system is consistent because with three pivots,