# Thread: Invertible & examining the image through the unit square

1. ## Invertible & examining the image through the unit square

let f : $R^2 \rightarrow R^2$ be defined by f(x,y) = (x+y, 2x+ay) where a $\in$ R is a constant.

(a) Show that df(x,y) is invertible if and only if a $\neq$ 2
(b) Examine the image through f of the unit square Q :={(x,y) $\in$ [0,1] x [0,1]} when a=1, a=2, and a=3

So.. I don't understand how to show it's invertible or what (b) even means...

2. Notice that f is a linear transformation.
for(1), you need to find the matrix correspondding to f.
for(2), find the four image of the four vertex of each unit square.

3. yeah... if I learned that, I don't recall it...

I'm still lost