Question: Let V be a vector space over F. First, show the Cancellation law for vector addition i.e. given u, U, w E V, show that

Let V be a vector space over F. First, show the Cancellation law for vector addition i.e. given u, U, w E V, show that if u + v = u + w then we have v = w. Then using that to show the following properties of a vector space: 1. The zero vector 0 in VS3 is unique. 2. The additive inverse v' in VS4 is unique, i.e. for each v E V there exists a unique vector U' E V such that u + v' = 0. Denote v' as -v. 3. Ou = 0 for all v E V. 4. (-A)u = -(10) = A(-v) for all v E V and 1 E F. 5. 10 = 0 for all 1 E F

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