LetVbe the set of all ordered pairs of real numbers (u₁,u₂) withu₂> 0. Consider the following addition and scalar multiplication operations onu= (u₁,u₂) andv= (v₁,v₂):

u+v= (u₁+v₁+ 4,7u₂v₂),ku= (ku₁,ku₂)

Use the above operations for the following parts.

(a)If the setVsatisfies Axiom 4 of a vector space (the existence of a zero vector), what would be the zero vector?

(b)Ifu= (5,3), what would be the negative of the vectorureferred to in Axiom 5 of a vector space?

(Don't forget to use your answer to part (a) here!)