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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 v₁ and v₂ are in R4 and v₂ is not a scalar multiple of v₁, then {V₁, V₂} is linearly independent. 1: Choose the correct answer below. 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. OB. The statement is false. The vector v₁ could be the zero vector. O C. The statement is false. The vector v₁ could be equal to the vector V2. O D. The statement is false. The vector v₁ could be a scalar multiple of vector v₂.

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 v₁ and v₂ are in R4 and v₂ is not a scalar multiple of v₁, then {V₁, V₂} is linearly independent. 1: Choose the correct answer below. 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. OB. The statement is false. The vector v₁ could be the zero vector. O C. The statement is false. The vector v₁ could be equal to the vector V2. O D. The statement is false. The vector v₁ could be a scalar multiple of vector v₂.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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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 v₁ and v₂ are in Rª and v₂ is not a scalar multiple of v₁, then {V₁, 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. B. The statement is false. The vector v₁ could be the zero vector. C. The statement is false. The vector v₁ could be equal to the vector V2. O D. The statement is false. The vector v₁ could be a scalar multiple of vector v₂.
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 v₁ and v₂ are in Rª and v₂ is not a scalar multiple of v₁, then {V₁, 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. B. The statement is false. The vector v₁ could be the zero vector. C. The statement is false. The vector v₁ could be equal to the vector V2. O D. The statement is false. The vector v₁ could be a scalar multiple of vector v₂.
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