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1. (a) Find an example of a set of vectors in R³ that is linearly independent but does not span R°. (b) Find an example of a set of vectors in R3 that spans R3 but is not linearly independent. (c) Let S = {v1,· , vn} be a set of n vectors in R". Show that S is linearly independent if and only if S spans R". ...

1. (a) Find an example of a set of vectors in R³ that is linearly independent but does not span R°. (b) Find an example of a set of vectors in R3 that spans R3 but is not linearly independent. (c) Let S = {v1,· , vn} be a set of n vectors in R". Show that S is linearly independent if and only if S spans R". ...

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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4. (a) Find an example of a set of vectors in R³ that is linearly independent but does not span R. (b) Find an example of a set of vectors in R³ that spans R3 but is not linearly independent. (c) Let S = {v1, · · , vn} be a set of n vectors in R". Show that S is linearly independent if and only if S spans R".
Transcribed Image Text:4. (a) Find an example of a set of vectors in R³ that is linearly independent but does not span R. (b) Find an example of a set of vectors in R³ that spans R3 but is not linearly independent. (c) Let S = {v1, · · , vn} be a set of n vectors in R". Show that S is linearly independent if and only if S spans R".
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