I think you can try to use MATLAB, it has nice build-in routines especially for linear (matrix) algebra. I just used its build-in function “svd” to find the answers to your question. The singular values of this matrix are: and .

We can also use the build-in function “inv” to find the inverse of a given matrix. The inverse to your question is

You might following links are useful:

MATLAB (svd)

MATLAB (inv)

Roy