Let [math]. For [math] and [math] define vector addition by [math] and scalar multiplication by [math]. It can be shown that [math] is a vector space over the scalar field [math]. Find the following:

the sum:

[math]( , )

the scalar multiple:

[math]( , )

the zero vector:

[math]( , )

the additive inverse of [math]:

[math]( , )