Unformatted text preview: (b) Now suppose −→ u , −→ v and −→ w are three nonzero vectors in R 3 . If −→ v and −→ w are linearly independent, show that every vector lying in the plane that contains the two lines through the origin parallel to −→ v and −→ w can be expressed as a linear combination of −→ v and −→ w . Now show that if −→ u does not lie in this plane, then every vector in R 3 can be expressed as a linear combination of −→ u , −→ v and −→ w . The two statements above are summarized by saying that −→ v and −→ w ( resp . −→ u , −→ v and −→ w ) span R 2 ( resp . R 3 ). Challenge problem:...
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 Fall '08
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 Calculus, Linear Algebra, Addition, Vectors, Scalar, Vector Space, Linear combination, linearly independent vectors

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