Undergrad True or False: A Linear System Must Have a Unique Solution

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A linear system with homogeneous equations always has at least the trivial solution, but it can also have infinitely many solutions. The statement that such a system must have a unique solution is therefore false. The confusion arises from the book's assertion that the answer is true, which contradicts the understanding of linear systems. This discrepancy can undermine student confidence in the material. Overall, the book's answer is considered incorrect by the discussion participants.
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So I'm reading chapter 1.1 of Elementary Linear Algebra by Anton and there's this true-false question:

"A linear system whose equations are all homogenous must have a unique solution."

Taking this question simply as it is I think the answer should be false, because while there's always the trivial solution, it's also possible for there to be infinite solutions. Yet the book gives the answer as True? I think it's pretty confusing and doesn't give the student confidence when the very first question has the wrong answer.
 
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The book is wrong.
 

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