Hi,

The Question:

A transformation $\displaystyle x \rightarrow Ax$ sends vector $\displaystyle (1,0)^T$ to $\displaystyle (3,-2)^T$ and vector $\displaystyle (0,-1)^T$ to $\displaystyle (2,-1)^T$. What is $\displaystyle A$? Find the inverse of $\displaystyle A$.

This is what I thought you're supposed to do:

Let $\displaystyle A = (x,y)^T$. Therefore:

$\displaystyle (1,2)^T (x,y)^T = (3,-2)^T$

$\displaystyle (0,-1)^T (x,y)^T = (2,-1)^T$

I thought I could solve for $\displaystyle x, y$ simultaneously but I really don't know where to go .

Thanks