Why is the answer B? True or False: Whenever a system has free variables, the solution set contains many solutions. Choose the correct answer below. A. The statement is false. A system with one free variable will have only one solution. B. The statement is 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. C. The statement is true. If a solution has at least one free variable, there are infinitely many solutions. D. The statement is true. If there are infinitely many solutions, then there must be at least one free variable.
Why is the answer B? True or False: Whenever a system has free variables, the solution set contains many solutions. Choose the correct answer below. A. The statement is false. A system with one free variable will have only one solution. B. The statement is 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. C. The statement is true. If a solution has at least one free variable, there are infinitely many solutions. D. The statement is true. If there are infinitely many solutions, then there must be at least one free variable.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Why is the answer B?
True or False: Whenever a system has free variables, the solution set contains many solutions. Choose the correct answer below.
The statement is false. A system with one free variable will have only one solution.
The statement is 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.
The statement is true. If a solution has at least one free variable, there are infinitely many solutions.
The statement is true. If there are infinitely many solutions, then there must be at least one free variable.
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