Let V be a vector space and suppose that {u, v, w} is an independent set of vectors in V. For each of the following sets of vectors, determine whether it is linearly independent or linearly dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector. a) {2v+2w, -3u+2w, -3u-2v} < Select an answer >
Let V be a vector space and suppose that {u, v, w} is an independent set of vectors in V. For each of the following sets of vectors, determine whether it is linearly independent or linearly dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector. a) {2v+2w, -3u+2w, -3u-2v} < Select an answer >
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The first one is dependent and the second one is independent
If there is dependent, please find the coefficient
![Let V be a vector space and suppose that {u, v, w} is an independent set of vectors in V. For each of the following sets of vectors, determine whether it is linearly independent or linearly
dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector.
a) {2v+2w, -3u+2w, -3u-2v}
is linearly dependent
0 (2v+2w) + 0 (-3u+2w) + 0 (-3u-2v) = 0
b) {3v-w, -2u-3w, u+2v}
is linearly dependent
0 (3v-w) + 0 (-2u-3w) + 0 (u+2v) = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4703214b-7b6d-48dc-8fec-73bc2badaa48%2F5b1a234e-3af7-4b21-9212-809d370841b9%2Ftxkijzg_processed.png&w=3840&q=75)
Transcribed Image Text:Let V be a vector space and suppose that {u, v, w} is an independent set of vectors in V. For each of the following sets of vectors, determine whether it is linearly independent or linearly
dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector.
a) {2v+2w, -3u+2w, -3u-2v}
is linearly dependent
0 (2v+2w) + 0 (-3u+2w) + 0 (-3u-2v) = 0
b) {3v-w, -2u-3w, u+2v}
is linearly dependent
0 (3v-w) + 0 (-2u-3w) + 0 (u+2v) = 0
![Let V be a vector space and suppose that {u, v, w} is an independent set of vectors in V. For each of the following sets of vectors, determine whether it is linearly independent or linearly
dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector.
a) {2v+2w, -3u+2w, -3u-2v}
< Select an answer >
b) {3v-w, -2u-3w, u+2v}
< Select an answer >](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4703214b-7b6d-48dc-8fec-73bc2badaa48%2F5b1a234e-3af7-4b21-9212-809d370841b9%2Fl930szq_processed.png&w=3840&q=75)
Transcribed Image Text:Let V be a vector space and suppose that {u, v, w} is an independent set of vectors in V. For each of the following sets of vectors, determine whether it is linearly independent or linearly
dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector.
a) {2v+2w, -3u+2w, -3u-2v}
< Select an answer >
b) {3v-w, -2u-3w, u+2v}
< Select an answer >
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