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3. Recall that for a subspace U CR", its orthogonal complement U is U = {ve R" | u v=0 for all u € U}. Suppose that v and v' are non-zero vectors in Rn such that v EU and v' e U. Show that v and v' are linearly independent.

3. Recall that for a subspace U CR", its orthogonal complement U is U = {ve R" | u v=0 for all u € U}. Suppose that v and v' are non-zero vectors in Rn such that v EU and v' e U. Show that v and v' are linearly independent.

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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3. Recall that for a subspace U CR", its orthogonal complement U is U = {ve R" | u v=0 for all u € U}. Suppose that v and v' are non-zero vectors in Rn such that v EU and v' e U. Show that v and v' are linearly independent.
Transcribed Image Text:3. Recall that for a subspace U CR", its orthogonal complement U is U = {ve R" | u v=0 for all u € U}. Suppose that v and v' are non-zero vectors in Rn such that v EU and v' e U. Show that v and v' are linearly independent.
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