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Solved: cises 33–38 is either true (in all cases) or false
Chapter 1, Problem 37E(choose chapter or problem)
PROBLEM 37EEach statement in Exercises 33–38 is either true (in all cases) or false (for at least one example). If false, construct a specific example to show that the statement is not always true. Such an example is called a counterexample to the statement. If a statement is true, give a justification. (One specific example cannot explain why a statement is always true. You will have to do more work here than in Exercises 21 and 22.)If v1,…, v4 are in ?4 and { v1, v2, v3} is linearly dependent, then { v1, v2, v3, v4} is also linearly dependent.
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QUESTION:
PROBLEM 37EEach statement in Exercises 33–38 is either true (in all cases) or false (for at least one example). If false, construct a specific example to show that the statement is not always true. Such an example is called a counterexample to the statement. If a statement is true, give a justification. (One specific example cannot explain why a statement is always true. You will have to do more work here than in Exercises 21 and 22.)If v1,…, v4 are in ?4 and { v1, v2, v3} is linearly dependent, then { v1, v2, v3, v4} is also linearly dependent.
ANSWER:SOLUTIONStep 1If v1,…, v4 are in 4 and { v1, v2, v3} is linearly dependent, then { v1, v2, v3, v4} is also linearly dependent.