Chapter 1.1, Problem 31E

In Exercises 27—34, 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 the statement is not true in all cases.) Similar true/false questions will appear in many sections of the text and will be flagged with a (T/F) at the beginning of the question.

31. (T/F) The solution set of a linear system involving variables $x_1,\dots ,x_n$ is a list of numbers $s_1,\dots ,s_n$ that makes each equation in the system a true statement when the values $s_1,\dots ,s_n$ are substituted for $x_1,\dots ,x_n$, respectively.