(3) Let V be a vector space over a field F. Suppose that a ? F,...

(3) Let V be a vector space over a field F. Suppose that a ? F, v ? V and av = 0. Prove that a = 0 or v = 0.

(4) Prove that for any field F, F is a vector space over F.

(5) Prove that the set V = {a0 + a1x + a2x 2 + a3x 3 | a0, a1, a2, a3 ? R} of polynomials of degree ? 3 is a vector space over R (with respect to the usual addition and scalar multiplication of polynomials).

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milcah answered 1 year ago

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