document.write( "Question 1175271: Question 3 (10 marks). In each of the following parts, say whether the set
\n" ); document.write( "W is a subspace of the vector space V . Justify your answer in each case.
\n" ); document.write( "All parts of the question carry equal marks.
\n" ); document.write( "(a) V = Rn, W is the set of solutions of the nonhomogeneous linear system
\n" ); document.write( "Ax = b, where A is an m  n matrix and b 2 Rm.
\n" ); document.write( "(b) V = C[0; 1], the space of all continuous functions de ned on the interval
\n" ); document.write( "[0; 1], and W is the set of all continuous functions f de ned on [0; 1]
\n" ); document.write( "such that f(c) 2 Q for a xed c 2 [0; 1].
\n" ); document.write( "(Recall that the interval [0; 1] is the set of numbers 0  x  1 and that
\n" ); document.write( "Q is the set of rational numbers).
\n" ); document.write( "(c) V = R2, W is the graph of the function f(x) = x.
\n" ); document.write( "(Recall the the graph of a function f : R ! R is de ned as the set of
\n" ); document.write( "points
\n" ); document.write( "f(x; y) : y = f(x)g:
\n" ); document.write( "The graph of f is a subset of R2.)
\n" ); document.write( "(d) V = R2, W is the graph of the function f(x) = x + x2. \n" ); document.write( "
Algebra.Com's Answer #800893 by ikleyn(52790)\"\" \"About 
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