1. ## Transformation of planes

A unit square in $\Re^2$ formed by vertices (0,0), (0,1), (1,0), (1,1).

how does the matrix
$\left(\begin{array}{cc}1&-1\\1&1\end{array}\right)$

transform the the square. Draw the transformed square.

Thanks!

2. Originally Posted by Linnus
A unit square in $\Re^2$ formed by vertices (0,0), (0,1), (1,0), (1,1).

how does the matrix
$\left(\begin{array}{cc}1&-1\\1&1\end{array}\right)$

transform the the square. Draw the transformed square.

Thanks!
Individually pre-multiply each of the vectors (0,0) , (0,1) , (1,0) and (1,1) by the matrix. Where do they get mapped? This should help you to draw the transformed square.

Hope this helps.

3. Thanks! if you have some random numbers in the 2x2 matrix, would it transform the unit square into a trianglele?