True/False: If true, justify your answer. If false, modify the bracketed statement to make the sentence true. a. If Ax = b has a unique solution, then [Ax = 0 has no solution (inconsistent).] b. If Ax = b has infinitely many solutions, then [Ax = 0 must have a nontrivial solution.] c. If a nonzero vector v exists such that Av = 0, then [both Ax = 0 and Ax = b must have infinitely many solutions.]

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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True/False: If true, justify your answer. If false, modify the bracketed statement to make the sentence true.

a. If Ax = b has a unique solution, then [Ax = 0 has no solution (inconsistent).]

b. If Ax = b has infinitely many solutions, then [Ax = 0 must have a nontrivial solution.]

c. If a nonzero vector v exists such that Av = 0, then [both Ax = 0 and Ax = b must have infinitely many solutions.]

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