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Each statement in Exercises 33–38 is either
Chapter 1, Problem 33E(choose chapter or problem)
PROBLEM 33E
Each 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,…, v2 are in ℝ4 and v3 = 2v1 + v2, then {v1 + v2 + v3 + v4} is linearly dependent.
Questions & Answers
QUESTION:
PROBLEM 33E
Each 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,…, v2 are in ℝ4 and v3 = 2v1 + v2, then {v1 + v2 + v3 + v4} is linearly dependent.
ANSWER:
Solution
Step 1:
Given : are in ℝ4 and
We have to check whether {} are linearly dependent.