Having some LaTeX issues so this might look a bit off

let = (1,0) and = (0,1) Show that for every , there exist unique scalars

and such that = +

would this be (1,0) + (0,1) = ( , 0) + (0, ) = ( , ) =

I'll start there, there are two more parts to the question but I will see if I have this part first.