6. Let V be a vector space and v1, v2, V3, V4 are vectors in V. Suppose that {v1, v2, V3} are linear dependent and {v2, v3, v4} are linear independent. Show that (i) vi is a linear combination of v2, V3, and (ii) v4 is not a linear combination of v1, v2, V3.
6. Let V be a vector space and v1, v2, V3, V4 are vectors in V. Suppose that {v1, v2, V3} are linear dependent and {v2, v3, v4} are linear independent. Show that (i) vi is a linear combination of v2, V3, and (ii) v4 is not a linear combination of v1, v2, V3.
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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![6. Let V be a vector space and v1, v2, V3, V4 are vectors in V. Suppose that {v1, v2, V3} are
linear dependent and {v2, v3, V4} are linear independent. Show that (i) vị is a linear
combination of v2, V3, and (ii) v¼ is not a linear combination of v1, v2, V3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7abbf2d5-6ef3-489c-b2da-4d9327a88b2a%2F6a57dd01-47da-4941-af4a-c4c35f405c06%2F7ueslew_processed.png&w=3840&q=75)
Transcribed Image Text:6. Let V be a vector space and v1, v2, V3, V4 are vectors in V. Suppose that {v1, v2, V3} are
linear dependent and {v2, v3, V4} are linear independent. Show that (i) vị is a linear
combination of v2, V3, and (ii) v¼ is not a linear combination of v1, v2, V3.
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