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.

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- March 5th 2009, 09:50 AMypatiaLinear Algebra.Linear Transformation.Help
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.

- March 5th 2009, 11:25 AMGrandadInverse Transformation
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:

Grandad - March 5th 2009, 11:43 AMypatia
- March 5th 2009, 12:20 PMPlato
The matrix is which is singular.

- March 5th 2009, 01:14 PMGrandadTransformation matrix