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4. Let V = R2. [a] Show that V is not a vector space over R with the following operations: (i) For a111,.r I = ($1,32],y =(y1,y2) E V, I $3; = (%9%#) (oterve that this is the midpoint of :r and 3;), (ii) For an}.r c E [R and :1: x ($1,132) E V, c+:r =(cr1,c:rg) [h] Consider the fomring two statements: (i) For aHIEV,theTeexistsaneEVsuchthate+:r=.1:. (ii) ThereeadstsaneEVsuchthatforallIEV,e+I=I. Show that the rst statement is true while the second one is false. Discuss the existence of a zero 1.rector