Standard matrix for linear transform

I have the following linear transformation F(1,1)=(1,0,-1) ,F(0,1)=(-1-1-0) how do i find the standard matrix for this, do i need to find F(1,0)? if i do how do i find F(1,0)?

Thanks!

Yes, you do.
To do this, you need to express (1, 0) as a linear combination of (1, 1) and (0, 1).
Note that (1, 0) = (1, 1) - (0, 1).

Thus:
F(1, 0)
= F((1, 1) - (0, 1))
= F(1, 1) - F(0, 1) <--[Since F is linear.]
= (1, 0, -1) - (-1, -1, 0)
= (2, 1, -1)

Thus, the standard matrix is A = [F(1, 0) F(0, 1)], which is the 3x2 matrix:
[2 -1]
[1 -1]
[-1 0]