Determine by inspection whether the vectors are linearly independent. Justify your answer. - 8 2 16 - 4 4 1 Choose the correct answer below. O A. The set is linearly dependent because neither vector is a multiple of the other vector. Two of the entries in the first vector are - 4 times the corresponding entry in the second vector. But this multiple does not work for the third entries. O B. The set is linearly independent because the first vector is a multiple of the other vector. The entries in the first vector are - 4 times the corresponding entry in the second vector. OC. The set is linearly independent because neither vector is a multiple of the other vector. Two of the entries in the first vector are - 4 times the corresponding entry in the second vector. But this multiple does not work for the third entries. O D. The set is linearly dependent because the first vector is a multiple of the other vector. The entries in the first vector are - 4 times the corresponding entry in the second vector.
Determine by inspection whether the vectors are linearly independent. Justify your answer. - 8 2 16 - 4 4 1 Choose the correct answer below. O A. The set is linearly dependent because neither vector is a multiple of the other vector. Two of the entries in the first vector are - 4 times the corresponding entry in the second vector. But this multiple does not work for the third entries. O B. The set is linearly independent because the first vector is a multiple of the other vector. The entries in the first vector are - 4 times the corresponding entry in the second vector. OC. The set is linearly independent because neither vector is a multiple of the other vector. Two of the entries in the first vector are - 4 times the corresponding entry in the second vector. But this multiple does not work for the third entries. O D. The set is linearly dependent because the first vector is a multiple of the other vector. The entries in the first vector are - 4 times the corresponding entry in the second vector.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 30RE
Related questions
Question
![**Determine by inspection whether the vectors are linearly independent. Justify your answer.**
\[
\left[
\begin{array}{r}
-8 \\
16 \\
4
\end{array}
\right],
\quad
\left[
\begin{array}{r}
2 \\
-4 \\
1
\end{array}
\right]
\]
Choose the correct answer below:
- **A.** The set is linearly dependent because neither vector is a multiple of the other vector. Two of the entries in the first vector are -4 times the corresponding entry in the second vector. But this multiple does not work for the third entries.
- **B.** The set is linearly independent because the first vector is a multiple of the other vector. The entries in the first vector are -4 times the corresponding entry in the second vector.
- **C.** The set is linearly independent because neither vector is a multiple of the other vector. Two of the entries in the first vector are -4 times the corresponding entry in the second vector. But this multiple does not work for the third entries.
- **D.** The set is linearly dependent because the first vector is a multiple of the other vector. The entries in the first vector are -4 times the corresponding entry in the second vector.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa204cf79-6df4-4f25-af61-d4fca6ca5b9e%2Fd45254f6-90e8-48f0-a269-2621332f01d8%2F0a6gx0c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determine by inspection whether the vectors are linearly independent. Justify your answer.**
\[
\left[
\begin{array}{r}
-8 \\
16 \\
4
\end{array}
\right],
\quad
\left[
\begin{array}{r}
2 \\
-4 \\
1
\end{array}
\right]
\]
Choose the correct answer below:
- **A.** The set is linearly dependent because neither vector is a multiple of the other vector. Two of the entries in the first vector are -4 times the corresponding entry in the second vector. But this multiple does not work for the third entries.
- **B.** The set is linearly independent because the first vector is a multiple of the other vector. The entries in the first vector are -4 times the corresponding entry in the second vector.
- **C.** The set is linearly independent because neither vector is a multiple of the other vector. Two of the entries in the first vector are -4 times the corresponding entry in the second vector. But this multiple does not work for the third entries.
- **D.** The set is linearly dependent because the first vector is a multiple of the other vector. The entries in the first vector are -4 times the corresponding entry in the second vector.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
