Linear Transformation in R2

[Idealistic]

let F:R[sup:35mj5o8y]2[/sup:35mj5o8y]->R[sup:35mj5o8y]2[/sup:35mj5o8y] be the nonlinear function defiend by f(x,y) = (xy,x[sup:35mj5o8y]2[/sup:35mj5o8y]). Let A be 2x2 matrix (F(x)= Ax) and show that A does not represent f. In otherwords, show that some x in R[sup:35mj5o8y]2[/sup:35mj5o8y], f(x) does not equal Ax.

Im just not sure how to construc the matrix, however I do know, that if f(x,y) = (x+y, x) it would look like this:

[1 + 1]
[1 0]

 

[chrisr]

\(\displaystyle The\ first\ step\ is\ A=\begin{bmatrix}y&0\\x&0\end{bmatrix}\)

\(\displaystyle \begin{bmatrix}y&0\\x&0\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}xy\\x^2\end{bmatrix}\)