Math  /  Algebra

QuestionLet u=[121],v=[000]\mathbf{u}=\left[\begin{array}{c}-1 \\ 2 \\ 1\end{array}\right], \mathbf{v}=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right], and w=[4216]\mathbf{w}=\left[\begin{array}{c}-4 \\ 2 \\ 16\end{array}\right] We want to determine by inspection (with minimal computation) if {u,v,w}\{\mathbf{u}, \mathbf{v}, \mathbf{w}\} is linearly dependent or independent. Choose the best answer. A. The set is linearly independent because we only have two vectors and they are not scalar multiples of each other. B. The set is linearly dependent because one of the vectors is the zero vector. 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 a scalar multiple of another vector. F. We cannot easily tell if the set is linearly dependent or linearly independent.

Studdy Solution
Conclude linear dependence or independence:
Since the set includes the zero vector v\mathbf{v}, the set {u,v,w}\{\mathbf{u}, \mathbf{v}, \mathbf{w}\} is linearly dependent.
The best answer is: B. The set is linearly dependent because one of the vectors is the zero vector.

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord