Howard S. Hamilton ........................................................................................hsh2760

Week 11 ...........................................................................................................7-2-6

http://www.cs.tamu.edu/people/hamilton/math-311/week11/7-2-6.html

Show that the determinate of a shear transformation is always 1.

Solution:

Given a 2x2 shear transformation:

The determinate of this matrix is easy to calculate as one:

(1*1) - (a*0) = 1

This also expands out to the 3x3 matrix:

1*(1-0) - a*(0) + b*(0) = 1

So in the general case of the NxN triangular matrix, the determinate
is the product of

the elements along the diagonal. In the case if the shear transformation,
this is N*(1).

So the determinate of a shear transformation is always 1.