o) Let v1, v2, V3 be three vectors in F and let W = span {v1, v2, V3}. O What is the largest possible number of vectors that W could contain? Briefly EX- PLAIN your answer. (You can just express your answer as a power of some number; you don't have to multiply out that power.) What condition can you put on the set {v1, V2, V3} that will ensure that W contains that largest possible number of vectors? Briefly EXPLAIN your answer.

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ISBN:9780470458365
Author:Erwin Kreyszig
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8. (!
-) Let v1, V2, V3 be three vectors in F, and let W = span {v1, v2, V3}.
(a) What is the largest possible number of vectors that W could contain? Briefly EX-
PLAIN your answer. (You can just express your answer as a power of some number;
you don't have to multiply out that power.)
(b) What condition can you put on the set {v1, V2, V3} that will ensure that W contains
that largest possible number of vectors? Briefly EXPLAIN your answer.
Transcribed Image Text:8. (! -) Let v1, V2, V3 be three vectors in F, and let W = span {v1, v2, V3}. (a) What is the largest possible number of vectors that W could contain? Briefly EX- PLAIN your answer. (You can just express your answer as a power of some number; you don't have to multiply out that power.) (b) What condition can you put on the set {v1, V2, V3} that will ensure that W contains that largest possible number of vectors? Briefly EXPLAIN your answer.
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