let u=[2,-1,-4], v=[0,0,0], and w=[-6,-9,8]. we want to determine by

he298c 2021-10-21 Answered
let \(\displaystyle{u}={\left[{2},-{1},-{4}\right]},{v}={\left[{0},{0},{0}\right]}\), and \(\displaystyle{w}={\left[-{6},-{9},{8}\right]}\). we want to determine by inspection (with minimal compulation) if \(\displaystyle{\left\lbrace{u},{v},{w}\right\rbrace}\) 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 the number of vectors in the set is greater than the dimension of the vector space.
D. The set is linearly dependent because two of the vectors are the same.
E. The set is linearly dependent because one of the vectors is the zero vector.
F. We cannot easily tell if the set is linearly dependent or linearly independent.

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Expert Answer

Derrick
Answered 2021-10-22 Author has 16336 answers
Step 1
Any set containing the zero vector is linearly dependent since in \(\displaystyle{\left\lbrace{u},{v},{w}\right\rbrace}\) the vector v is zero vector.
Step 2
So the set is linearly dependent because one of the vectors is the zero vector.
The correct option is E.
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