Exercises part 3

1. Here is a function declaration for flattening a List of Lists:

   flattenList : List (List a) -> List a
   

   Implement flattenList and declare and implement a similar function flattenVect for flattening vectors of vectors.

2. Implement functions take' and splitAt' like in the exercises of the previous section but using the technique shown for drop'.

3. Implement function transpose for converting an m x n-matrix (represented as a Vect m (Vect n a)) to an n x m-matrix.

   Note: This might be a challenging exercise, but make sure to give it a try. As usual, make use of holes if you get stuck!

   Here is an example how this should work in action:

   Solutions.Dependent> transpose [[1,2,3],[4,5,6]]
   [[1, 4], [2, 5], [3, 6]]