SOLUTION: Question 3 (10 marks). In each of the following parts, say whether the set W is a subspace of the vector space V . Justify your answer in each case. All parts of the question car

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

Formatting of the post is strange and UNREADABLE.

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