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Suppose that ú, v and w are any three vectors in some R". Show that the set of three vectors: S = {2ủ + v, 4ủ + 5v – 4w, ủ – v + 2w}, will always be a dependent set. Hint: form the dependence test equation involving these three new vectors and find a non-trivial solution.

Suppose that ú, v and w are any three vectors in some R". Show that the set of three vectors: S = {2ủ + v, 4ủ + 5v – 4w, ủ – v + 2w}, will always be a dependent set. Hint: form the dependence test equation involving these three new vectors and find a non-trivial solution.

Advanced Engineering Mathematics
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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Suppose that ủ, v and w are any three vectors in some R". Show that the set of three vectors: S = { 2ủ + v, 4ủ + 5v – 4w, ủ – v + 2w}, will always be a dependent set. Hint: form the dependence test equation involving these three new vectors and find a non-trivial solution. | 5.
Transcribed Image Text:Suppose that ủ, v and w are any three vectors in some R". Show that the set of three vectors: S = { 2ủ + v, 4ủ + 5v – 4w, ủ – v + 2w}, will always be a dependent set. Hint: form the dependence test equation involving these three new vectors and find a non-trivial solution. | 5.
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