Given is the transformation of coordinates $ T_{AB} = \begin{pmatrix} 1 & 1 \\ -1 & 1 \end{pmatrix} $.
1.) What are the new coordinates for the vectors (1,0) and (0,1)?
It should be:
$ \vec y = T_{AB} \cdot (1,0) = (1, -1)$ and
$ \vec y = T_{AB} \cdot (0,1) = (1,1)$. So these are the coordinates for the standard-basis.
2.) What are the new coordinates for the line $g: y = 2x-5$ ?
This line can also be written as $ g: \vec x = (0, -5) + r\cdot(1,2)$ (I took two points on the line).
Same procedure as in 1: then the new line is $ g': \vec x = (-5, -5) + s\cdot(3,1)$.
I'm really not sure if did this correct, so I really do need some help :)