Question: Problem 5. Prove that every vector space has a unique zero vector. [25 marks] Problem 6. Let -co and oo denote two distinct objects, neither

Problem 5. Prove that every vector space has a unique zero vector. [25 marks] Problem 6. Let -co and oo denote two distinct objects, neither of which is in R. Define an addition and scalar multiplication on RU{} U {-oo}. Specifically, the sum and product of two real numbers is as usual, and for te R define -OO if t 0, - OO if t > 0, t+ oo = 0ott = 00 , t+ ( -00 ) = - 00 + t = -00 , 00 + 00 = 00 , ( -00 ) + (-00 ) =-00 , 00 + ( -00 ) = 0 . Determine whether RU {oo} U {-oo} is a vector space over R. [25 marks]

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