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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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus, Vectors, Scalar

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