# Transformation of planes

• September 1st 2009, 02:33 PM
Linnus
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!
• September 1st 2009, 02:36 PM
pomp
Quote:

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.
• September 2nd 2009, 04:51 PM
Linnus
Thanks! if you have some random numbers in the 2x2 matrix, would it transform the unit square into a trianglele?