Nonstandard Definitions: In Problems 1-2 we explore the possibility of defining a new vector space whose vectors

Question:

Nonstandard Definitions: In Problems 1-2 we explore the possibility of defining a new vector space whose vectors are the familiar pairs (x, y) of real numbers but for which different operations are defined. (We are not in R2 any more, Toro!) For the operations given in each problem, decide whether the vector space requirements hold?