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Unformatted text preview: 1 11 1 where k is a constant. This tells us thatv 1 + v 2v 3 + v 4 = 0. Therefore, they are not linearly independent. No solution exists for 1 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 c 1 c 2 c 3 c 4 = 1 so they do not span R 4 . Problem 2.3.26 a) True, any vector linearly independent of the basis vectors for S will extend the basis to R 6 . b) False, because the basis vectors may not be in S . Problem 2.3.42 Basis 1 , x, x 2 , x 3 ; basis x1 , x 21 , x 31 when p (1) = 0. 2...
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 Spring '08
 Neely
 Linear Algebra, basis, basis vectors, Dr. Jonckheere TA, Ben Raskob

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