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5. ints) Let v1,..., Un be vectors in a vector space V. Suppose w is another vector in V. Determine whether or not the statement: "Span(u,..., ,) = Span(ī1,..., Un, w) if and only if 71,..., Tn, w are linearly depen- dent." is always true. If it is true, prove it. If it is false, provide an example showing why it is false.

5. ints) Let v1,..., Un be vectors in a vector space V. Suppose w is another vector in V. Determine whether or not the statement: "Span(u,..., ,) = Span(ī1,..., Un, w) if and only if 71,..., Tn, w are linearly depen- dent." is always true. If it is true, prove it. If it is false, provide an example showing why it is false.

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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5. ints) Let v1,..., Un be vectors in a vector space V. Suppose w is another vector in V. Determine whether or not the statement: "Span(71, dent." In) = Span(T1,..., Tn, w) if and only if i,. Un, w are linearly depen- .... ... is always true. If it is true, prove it. If it is false, provide an example showing why it is false.
Transcribed Image Text:5. ints) Let v1,..., Un be vectors in a vector space V. Suppose w is another vector in V. Determine whether or not the statement: "Span(71, dent." In) = Span(T1,..., Tn, w) if and only if i,. Un, w are linearly depen- .... ... is always true. If it is true, prove it. If it is false, provide an example showing why it is false.
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