Suppose T is the linear transformation on R^3 that takes each point (x,y,z) to (x+y+z, x+y,z). Describe what T^-1 does to the point (x,y,z). Thanks in advance.
Hello ypatiaDo you know how to find the inverse of a 3x3 matrix? There are quite a few web-sites that will explain the method, if you don't. Just Google 'Inverse of a 3x3 matrix'.
In the question you have here, the transformation can be written in matrix form as
So, to find the inverse transformation, you'll need the inverse of the matrix , which is
To find its effect on , just do the matrix multiplication:
So there's your answer: x,y,z) \rightarrow (z,y-z,x-y)" alt="T^{-1}x,y,z) \rightarrow (z,y-z,x-y)" />
Grandad