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**Unformatted text preview: **Homework Set 4 for MAS 4105
Due Friday, February 10
1. Deﬁne V = {f ∈ P3 (R) : f ′ (−2) = 0}.
(a) Compute dim(V ).
(b) Find subspaces W1 and W2 of V such that dim(W1 ) = 1 and
dim(W2 ) = 2.
(Problem 2 on Homework Set 3 may be helpful here.)
2. Let V be a vector space over F . Prove that V is inﬁnite-dimensional
if and only if V contains an inﬁnite linearly independent subset.
The following problems are strongly recommended, but should not be
turned in:
1.6: 1efghjkl
2.1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16 ...

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