Determine by inspection whether the vectors are linearly independent. Justify your answer. 50 9 4 6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The set of vectors is linearly dependent because times the first vector is equal to the second vector. (Type an integer or a simplified fraction.)
Determine by inspection whether the vectors are linearly independent. Justify your answer. 50 9 4 6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The set of vectors is linearly dependent because times the first vector is equal to the second vector. (Type an integer or a simplified fraction.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 45E
Related questions
Question
![### Linear Independence of Vectors
#### Problem Statement:
Determine by inspection whether the vectors are linearly independent. Justify your answer.
Given Vectors:
\[ \left[ \begin{array}{c} 6 \\ -12 \\ 9 \end{array} \right] \text{ and } \left[ \begin{array}{c} 4 \\ -8 \\ 6 \end{array} \right] \]
#### Instructions:
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Options:
A. The set of vectors is linearly dependent because \(\boxed{\phantom{1}}\) times the first vector is equal to the second vector. (Type an integer or a simplified fraction.)
B. The set of vectors is linearly dependent because neither vector is the zero vector.
C. The set of vectors is linearly independent because neither vector is a multiple of the other vector.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8109dbb5-39b2-442d-b17d-793e299fca4a%2Ffe769eb2-102f-49dd-8b67-6d8ac094890b%2Fnxnjqn6_processed.png&w=3840&q=75)
Transcribed Image Text:### Linear Independence of Vectors
#### Problem Statement:
Determine by inspection whether the vectors are linearly independent. Justify your answer.
Given Vectors:
\[ \left[ \begin{array}{c} 6 \\ -12 \\ 9 \end{array} \right] \text{ and } \left[ \begin{array}{c} 4 \\ -8 \\ 6 \end{array} \right] \]
#### Instructions:
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Options:
A. The set of vectors is linearly dependent because \(\boxed{\phantom{1}}\) times the first vector is equal to the second vector. (Type an integer or a simplified fraction.)
B. The set of vectors is linearly dependent because neither vector is the zero vector.
C. The set of vectors is linearly independent because neither vector is a multiple of the other vector.
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