If $\displaystyle F$ is a field and $\displaystyle f$ is the linear functional on $\displaystyle F^2$ s.t. $\displaystyle f(x_1,x_2) = ax_1+bx_2$

For the following linear operators $\displaystyle T$, let $\displaystyle g = T^{t}f $and find $\displaystyle g(x_1,x_2)$

lets say $\displaystyle T(x_1,x_2) = (x_1,0)$

So do I find $\displaystyle f$ first, get $\displaystyle f(x_1,x_2) = ax_1+bx_2$

do i now treat "$\displaystyle ax_1$" and "$\displaystyle bx_2$" as a vector with two rows and multiply by the transpose of the matrix representation of the linear transformation?

in this case, i get $\displaystyle ax_1$

I read this part of the book, it really isn't clear on what to do. Thank you for your help.