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  3. let v r2 with the following operations z y...

Question: let v r2 with the following operations z y...

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Let V = R2 with the following operations: (zı, yı) + (2 2,32) = (x1 +T2-1, yı +B2) (addition) c(x1, y) = (czi-e+ 1, cy) where c E R (scalar multiplication). Then V is a vector space with these operations (you can take this as given). (a) (2) Let (-2,4) and (2,3) belong to V and let c -2 R. Find ca + y using the operations defined on V. (b) (2) What is the zero vector in V? Justify. (c) (2) If 코= (-3,2), what is the additive inverse ofz? Justify (d) (2) For an arbitrary vector = (zi,yi), what is the additive inverse of z? Justify. (e) (3) Prove property 7. for vector spaces: If c E R and (,v), (x2,y2) E V, then c(z+め= cz +cji (Hint. work out both sides of the equation separately to show they are equal.)
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