6. given vector spaces u and v over the same field f, we can construct a new vector space ux v over f, which we call the cartesian product of u and v as follows. define with addition and scalar multiplication defined by you may take it for granted that this is a vector space over f (a) in the vector space p2(r) x r? , compute 132 (b) for any two vector spaces u and v over f, what is the zero vector in u x v? justify your answer. (c) suppose u has basis (n, . . ,%) and v has basis {n, ,fm). find a basis for u x v what is the dimension of ux v?