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.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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