Before revision:  A direct application of the algorithm is the 3-SAT problem, which is also guaranteed to be in the class P with a computational complexity of order O n^{\frac{45{2}}}  . The algorithm was implemented in MATLAB and checked by generating one million matrices of arbitrary dimension up to 24 with random entries in the range \left[ -50,50\right] . All the experiments were successful .
After revision:  A direct application of the algorithm is the 3-SAT problem, which is also guaranteed to be in the class P with a computational complexity of order O n^{\frac{45{2}}} . The algorithm was implemented in MATLAB and checked by generating five million matrices of arbitrary dimension up to 24 with random entries in the range \left[ -50,50\right] . All the experiments were successful .