Let u = 1 -3 V = -5 2 8 0 and w= -1 We want to determine by inspection (with minimal computation) if {u, v, w} is linearly dependent or independent. Choose the best answer. OA. The set is linearly dependent because one of the vectors is a scalar multiple of another vector. B. The set is linearly independent because we only have two vectors and they are not scalar multiples of each other. C. The set is linearly dependent because one of the vectors is the zero vector. D. The set is linearly dependent because two of the vectors are the same. O E. The set is linearly dependent because the number of vectors in the set is greater than the dimension of the vector space. OF. We cannot easily tell if the set is linearly dependent or linearly independent.
Let u = 1 -3 V = -5 2 8 0 and w= -1 We want to determine by inspection (with minimal computation) if {u, v, w} is linearly dependent or independent. Choose the best answer. OA. The set is linearly dependent because one of the vectors is a scalar multiple of another vector. B. The set is linearly independent because we only have two vectors and they are not scalar multiples of each other. C. The set is linearly dependent because one of the vectors is the zero vector. D. The set is linearly dependent because two of the vectors are the same. O E. The set is linearly dependent because the number of vectors in the set is greater than the dimension of the vector space. OF. We cannot easily tell if the set is linearly dependent or linearly independent.
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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Transcribed Image Text:Let **u** = \(\begin{bmatrix} 1 \\ -3 \\ -5 \end{bmatrix}\), **v** = \(\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}\), and **w** = \(\begin{bmatrix} 2 \\ -1 \\ -5 \end{bmatrix}\).
We want to determine by inspection (with minimal computation) if {**u**, **v**, **w**} is linearly dependent or independent.
Choose the best answer.
- A. The set is linearly dependent because one of the vectors is a scalar multiple of another vector.
- B. The set is linearly independent because we only have two vectors and they are not scalar multiples of each other.
- C. The set is linearly dependent because one of the vectors is the zero vector.
- D. The set is linearly dependent because two of the vectors are the same.
- E. The set is linearly dependent because the number of vectors in the set is greater than the dimension of the vector space.
- F. We cannot easily tell if the set is linearly dependent or linearly independent.
Expert Solution
Step 1: Our Aim
We have to decide whether the given three vectors u, v, w are linearly independent or linearly dependent.
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