a. Let V be any finite dimensional vector space. In class, we learned that for any finite set (w1, w2, - , wk) of vectors, W = span(w1, w2, ..., Wk) is a subspace of V. In other words, ...) If there is a finite set (w1, W2, . . . , Wk), then W = span(w1, w2, ... , Wk) is a subspace of V. Is the following statement correct? Why or why not? If W is a subspace of V, then there is a finite set (w1, w2, . , Wk) so that W span(w1, w2, ...,

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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write an explanation in full sentences

a. Let V be any finite dimensional vector space. In class, we learned that for any finite set
(w1, w2, ... , Wk) of vectors, W = span(w1, w2, .
Wk) is a subspace of V. In other words,
... )
If there is a finite set (w1, w2, . .. , Wk),
then W = span(w1, w2, .
Wk) is a subspace of V.
...
Is the following statement correct? Why or why not?
If W is a subspace of V,
then there is a finite set (w1, W2, -
Wk) so that W = span(w1, w2,
Wk).
Transcribed Image Text:a. Let V be any finite dimensional vector space. In class, we learned that for any finite set (w1, w2, ... , Wk) of vectors, W = span(w1, w2, . Wk) is a subspace of V. In other words, ... ) If there is a finite set (w1, w2, . .. , Wk), then W = span(w1, w2, . Wk) is a subspace of V. ... Is the following statement correct? Why or why not? If W is a subspace of V, then there is a finite set (w1, W2, - Wk) so that W = span(w1, w2, Wk).
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