write function as sum of covectors

Question

I've got what should be a simple question. I have a function f(x,y) = 3x + 2y

The question asks to write this function as a sum of dual vectors. Any help on where to begin?

Answer 1

Try the dual vectors of the canonical basis $\{e_1,e_2\}$ of $\mathbb{R}^2$. Observe that $e^1(x,y)=x$ and $e^2(x,y)=y$.