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Unformatted text preview: (b) Prove that the nullspace of an m × n matrix A is a subspace of R n . 4. (8 points) (a) Deﬁne the Span of a set { v 1 ,..., v n } . (b) Let f ( x ) = x and g ( x ) = e x and consider the subspace W =Span( f,g ) of C [0 , 1]. Prove that the functions h ( x ) = x + e x and k ( x ) = xe x span W . 1 2 5. (9 points) (a) Deﬁne the term subspace . (b) Let B be a ﬁxed 2 × 2 matrix. Prove that the set S = { C ∈ R 2 × 2  BC = 0 } is a subspace of R 2 × 2 . 6. (8 points) (a) Deﬁne the term linear independence . (b) Suppose v 1 , v 2 , v 3 are linearly independent vectors in a vector space V . Prove that the vectors v 1 + 2 v 2 , v 1v 2 , v 3 are linearly independent....
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This note was uploaded on 12/27/2011 for the course MAS 4105 taught by Professor Rudyak during the Spring '09 term at University of Florida.
 Spring '09
 RUDYAK

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