1. Decide if the following statement is True or False: Let R+ = {r ERr > 0}, and V = (Rt)" = {(x1, . .., In) | xi E Rt for each i}. Define a vector sum operation +' and a scalar multiplication operation .' by: (21 , . . ., Xn) + (y1 , . . . , yn) = (2191, . .., anyn), c . ' ( 2 1 , . . . , an ) = (21 , .. . , ." ) . Then V is a vector space with these two operations. Indicate your final answer by filling in exactly one circle below (unfilled o filled .) and justify your choice with a proof or counter-example. 5 marks] O True O False