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Application: Unblocked LU Factorization                                 [TOC]
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Implement the unblocked LU factorization with partial pivoting and demonstrate
on a small example that it works.

If you want: Develop your solution in an iterative process which is outlined in
the following.

Setup a matrix
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In `main`:

- Use and initialize some variables for matrix dimensions and increments
- Initialize a pointer for the first matrix element with dynamically allocated
  memory
- Initialize the matrix with some values.
- Print the matrix.

LU factorization without pivoting
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Implement the LU factorization without pivoting:

- Solve your example problem with pencil and paper
- Setup a function for this
- Copy and paste the BLAS functions needed
- Implement the function
- Make changes in `main` such that it print the matrix before and after the
  factorization.
- Check your results.

You can subdivide the implementation of the LU factorization in even more
steps.