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If v, and vz are in R“ and v, is not a scalar multiple of v, , then {v, v2} is linearly independent. Choose the correct answer below. O A. The statement is true. A set of vectors is linearly independent if and only if none of the vectors are a scalar multiple of another vector. O B. The statement is false. The vector y could be a scalar multiple of vector v,. OC. The statement is false. The vector v, could be equal to the vector v. O D. The statement is false. The vector v, could be the zero vector.

If v, and vz are in R“ and v, is not a scalar multiple of v, , then {v, v2} is linearly independent. Choose the correct answer below. O A. The statement is true. A set of vectors is linearly independent if and only if none of the vectors are a scalar multiple of another vector. O B. The statement is false. The vector y could be a scalar multiple of vector v,. OC. The statement is false. The vector v, could be equal to the vector v. O D. The statement is false. The vector v, could be the zero vector.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
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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The following statement 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. If v, and v, are in R* and v, is not a scalar multiple of v, , then {v, v2} is linearly independent. Choose the correct answer below. O A. The statement is true. A set of vectors is linearly independent if and only if none of the vectors are a scalar multiple of another vector. O B. The statement is false. The vector v, could be a scalar multiple of vector v,. OC. The statement is false. The vector v, could be equal to the vector v,. O D. The statement is false. The vector v, could be the zero vector.
Transcribed Image Text:The following statement 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. If v, and v, are in R* and v, is not a scalar multiple of v, , then {v, v2} is linearly independent. Choose the correct answer below. O A. The statement is true. A set of vectors is linearly independent if and only if none of the vectors are a scalar multiple of another vector. O B. The statement is false. The vector v, could be a scalar multiple of vector v,. OC. The statement is false. The vector v, could be equal to the vector v,. O D. The statement is false. The vector v, could be the zero vector.
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