What is meant by "The scalar multiplication for this system is defined in an unusual way" is that you do not use (which is the classical product) but , that's all. The product is the usual product of real numbers.
Let V be the set of all ordered pairs of real numbers with addition defined by
(x1, x2) + (y1, y2) = (x1 + y1, x2 + y2)
and scalar multiplication defined by
α¤(x1, x2) = (αx1, x2)
The scalar multiplication for this system is defined in an unusual way, and consequently we use the symbol ¤ to avoid confusion with the ordinary scalar multiplication of vectors. Is V a vector space with these operations? Justify your answer.
I honestly would think not because α(x1, x2) should equal (αx1, αx2) however the problem states it is not ordinary scalar multiplication. It doesn't state what kind though . Help would be appreciated, thank you!