Question: 2. a) Prove that a subset W of a vector space V is a subspace of V if and only if 0 W and cu+v

2.

a) Prove that a subset W of a vector space V is a subspace of V if and only if 0 W and cu+v W whenever c F and u, v W.

( b) Use the theorem in ( a) to show that the subset W of R^3 defined by W={( 3t, 0, -2t : t R} is a subspace of V. Describe W geometrically and determine dim (W).

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