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Unformatted text preview: R 3 which satisfy u Â· x = 3, where u = 1 1 1 . 4. Show that if V,W âŠ‚ R n are linear subspaces then V âˆ© W is as well a linear subspace of R n . 1 5. Let v 1 = 1 11 and v 2 = 11 2 and V = span { v 1 , v 2 } , which of the following vectors are in V ? 1 1 , 2 5 , 23 9 3144 6. Are the following sets of vectors linearly dependent or independent? (a) Â± 2 1 Â² , Â±147 Â² (b) Â± 11 Â² , Â±1 2 Â² (c) 11 1 , 1 1 1 , 2 2 7. Show that if the k vectors v 1 , v 2 Â·Â·Â· v k âˆˆ R n are all nonzero and mutually orthogonal, i.e., v i Â· v k = 0 if i 6 = k , then they are linearly independent. 2...
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 Spring '10
 Spyros
 Linear Algebra, Algebra, Geometry, Vectors, Dot Product, Articles containing proofs, Cauchy Schwarz inequality

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