Math 205a Quiz 05 Worksheet - Bates College, 2008

Math 205A

Quiz 05 page 1

October 24, 2008

NAME

1. Suppose V is a vector space and H is a subset of V . What are the three properties that H must

satisfy in order to be a subspace of V ? (List in the same order as we have in class)

(1)

(2)

(3)

2. As in class, let F be the vector space whose members are functions f : R → R which are continuous.

The ﬁgure below shows the graphs of two vectors u and v in F. On the empty grid to the right, show the

graph of

2v. On the bottom grid, show the linear combination u + v. (Draw both answers with solid

lines)

3. Let H be the subset of all vectors in F whose graph is horizontal from x = 1 to x = 3.

3a. Is either of u or v from problem (2) in H? Explain both decisions.

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