Our second project is intended to provide our own linear algebra classes (n-dim vector and nxm dim matrix) [based on our in-class V excersices]. Your classes should be implemented (each class a header and a source file) and your test program should use your classes via a shared library (Tip: test and debug your classes + test program via our modular approach, see Lec 5).

- Your vector class should use a dynamically allocated array
- Your Matrix class should use the STL vector class to implement a "2d array" (see in-class 5)

Functionalities of the vector class:
All standard operators (and also length, ...) should be defined, in addition for dimensions 2 and 3 define also the vector product.

Functionalities of the matrix class:
All standard operators for matrix and matrix/vector operations should be defined. Implement checks based on the operations if they are allowed given the dimension of the matrix/vector. Allow the matrix class to be a nxm dimensional matrix.
Also implement:
- the transposed matrix.
- the determinant of a matrix: The simplest implementation (the one you should use) utilizes a recursion algorithm (have a look at the example program section for a simple recursion program).

In addition (as a very good excercise but not necessary) try to implement for the simplest cases a matrix inversion.

Use as a test matrix:

1 3 3
1 4 3
1 3 4