Let x a b c d 1 2 3 4 what is the dimension

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Unformatted text preview: an (X)? Solution b) 10. Define subsets S1 , S2 , S3 of the function space F as follows: S1 = {f F | f (3) = 0} S2 = {f F | f (x) = 3 for all x R} S3 = {f F | f (3) = f (-3)} Which one of the following statements is true? a) b) c) d) S1 and S2 are subspaces of F, but S3 is not a subspace of F. S1 and S3 are subspaces of F, but S2 is not a subspace of F. S1 is a subspace of F, but S2 and S3 are not subspaces of F. None of these sets is a subspace of F. Solution b) 11. Suppose u, v, w, x are non-zero vectors in a vector space V , and that x is in Span {u, v, w} but x is not in Span {u, v}. Which one of the following statements is not correct? a) Span {u, v, x} =Span {u, v, w}. b) w is not in Span {u, v}. c) x must be a scalar multiple of w. d) {u, w} is a linearly independent set. Solution c) 12. Suppose A is a 4 6 matrix. Which one of the following is correct? a) Null(A) R4 and Col(A) R4 . b) Null(A) R6 and Col(A) R6 . c) Null(A) R6 and Col(A) R4 . d) Null(A) R4 and Col(A) R6 . Solution c) Math 2061...
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This note was uploaded on 02/06/2012 for the course MATH 2061 taught by Professor Notsure during the Three '09 term at University of Sydney.

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