1) Let V be the set of ordered pairs of real numbers: . Show

that V is not a vector space over with respect to each of the following

operations of addition in V and scalar multiplication in V:

2) Let . Show that W is not a subspace of V, where

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3) Find conditions on a, b and c so that belongs to the space generated

by , and .

4) Let V be the vector space of polynomials of degree over . Determine

whether are independent or dependent where

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5) Let W be the space generated by the polynomials: ,

, , . Find a

basis and the dimension of W.

6) Let U and W be the following subspaces of : ,

. Find a dimension and a basis of ,

and .

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