Solution Found!
Answer: In Exercises 23 and 24, key statements from this
Chapter 1, Problem 23E(choose chapter or problem)
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 the statement is not true in all cases.) Similar true/false questions will appear in many sections of the text.
a. Every elementary row operation is reversible.
b. A \(5 \times 6\) matrix has six rows.
c. The solution set of a linear system involving variables \(x_{1}, \ldots, x_{n}\) is a list of numbers \(\left(s_{1}, \ldots, s_{n}\right)\) that makes each equation in the system a true statement when the values \(S_{1}, \ldots, S_{n}\) are substituted for \(x_{1}, \ldots, x_{n}\) respectively.
d. Two fundamental questions about a linear system involve existence and uniqueness.
Questions & Answers
QUESTION:
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 the statement is not true in all cases.) Similar true/false questions will appear in many sections of the text.
a. Every elementary row operation is reversible.
b. A \(5 \times 6\) matrix has six rows.
c. The solution set of a linear system involving variables \(x_{1}, \ldots, x_{n}\) is a list of numbers \(\left(s_{1}, \ldots, s_{n}\right)\) that makes each equation in the system a true statement when the values \(S_{1}, \ldots, S_{n}\) are substituted for \(x_{1}, \ldots, x_{n}\) respectively.
d. Two fundamental questions about a linear system involve existence and uniqueness.
ANSWER:Solution: true/false questions
a. Every elementary row operation is reversible.
Step 1: True,every elementary row is reversible.
Explanation: If any matrix reverse multiplying by a constant by multiplying by its inverse.If we add row one to row two and replace row ,then subtract row one from row two to get it back.
b. A 5 × 6 matrix has six rows.
Example :
