Essay on Matrix Year 11 Draft for Reference(Not Plagiarism)

3256 WordsMay 14, 201314 Pages
Mat MPS 1 Part A: Determining fair rank between teams(no ties) Let win=3, draw=1 and lose=0. The reason for this weighting method is because it is natural for the loser not to get a point. Also, there must be a visible gap between winners and draw players. This can be proved by contradiction proof. Blue | B | Crimson | C | Green | G | Orange | O | Red | R | Yellow | Y | Assume that win=2 draw=1 and lose=0. If the supremacy matrix is calculated, tie always occurs, which proves that if there is a small gap between win and draws, that supremacy matrix isn’t valid. This is the teams and their initial letters, arranged by alphabetical order. Then, the diagraph below is converted into the following matrix. M=…show more content…
However, it is fair to provide lesser coefficient to M3, due to its relation with the original data. This means, the coefficient of M3 must be lesser than the first or second order Matrix. Therefore, the coefficient of M3 is 0.4, which is smaller than any of M or M2. S= M+0.5M2+0.4M3 = = The rank order is found as same as if the coefficient of M3 was different. The rank order is Oranges, Reds, Blues, Yellows, Crimsons and Greens. This rank has escalated the rank of Red Team into 2nd from 3rd, without any ties. This suggests the validity of the Supremacy Matris, S= M+0.5M2+0.4M3. Justification for the calculation The reason why I used S= M+0.5M2+0.4M3 is because of the reliability of the real data. In the dominance matrix M, not every cases are examined. However, even though escalating the coefficient can be considered as a solution, I chose to use M3 because if the rank order was same all the time in Supremacy Matrix including second-order matrix, I would have chose to increase the coefficient of M2. However, not every cases had same order. In fact, they had insufficient reliability to use as the Supremacy Matrix. As the alternative solution, M3 is used and it proved the efficiency of using M3 in the Supremacy Matrix. Also, as it can be seen in the second-order Supremacy Matrix, second-order Matrix has lesser coefficient. To keep this trend, M3 had lesser coefficient than M2, resulting the Supremacy Matrix of S=