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Unformatted text preview: such that u = .v ) c) for n > 1, ( v 1 , ..., v n ) is a linear dependent set if and only if one of the vector in the set v i is a linear combination of the other n-1 vectors. d)If ( v 1 , ..., v n ) is a linear independent set, and y is a dierent vector, ( v 1 , ..., v n , y ) is linearly dependent if and only if y is a linear combination of v 1 , ..., v n e) If ( v 1 , ..., v n ) is a linear independent set, then any subset of this set (such as v 1 , ..., v i , with i < n ) is also linear independent. 2 (5) Suppose we are in R 2 , what is the maximum number n of vectors that will make a linear independent set? Take show that any other vector can be expressed as a linear combination of these n linearly independent vectors. What about in R 3 ?...
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This note was uploaded on 08/01/2008 for the course ARE 211 taught by Professor Simon during the Fall '07 term at University of California, Berkeley.
- Fall '07