Question 3 For each of the following, explain whether it is (always) true or (possibly) false. If true, you must explain why. If false, you must give a concrete counterexample (with numbers). a) infinitely many solutions. b) must have a unique solution. c) If a linear system [ A | b] has fewer equations than variables then it has If [ A |b] has a unique solution, then the homogeneous system [ A | 0] Every 2x2 matrix satisfies (A)"= (A")².

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Question 3 For each of the following, explain whether it is (always) true or (possibly)
false. If true, you must explain why. If false, you must give a concrete counterexample
(with numbers).
a)
infinitely many solutions.
b)
must have a unique solution.
c)
If a linear system [ A | b] has fewer equations than variables then it has
If [ A |b] has a unique solution, then the homogeneous system A|0]
Every 2x2 matrix satisfies (A)"= (A')².
Transcribed Image Text:Question 3 For each of the following, explain whether it is (always) true or (possibly) false. If true, you must explain why. If false, you must give a concrete counterexample (with numbers). a) infinitely many solutions. b) must have a unique solution. c) If a linear system [ A | b] has fewer equations than variables then it has If [ A |b] has a unique solution, then the homogeneous system A|0] Every 2x2 matrix satisfies (A)"= (A')².
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