Transformation Matrix A and function phi

First we regard the standard system of linear equations most people would usually use. To do this, we assume that at the beginning all people do one certain activity, in the vector language this would be one standard basis vector from ... After this definition we can define that represents the state that all students go to the correct lecture.


The above in words : as said means that 100% of all students go to the lecture. The next time, and this is what phi() should calculate 70% of the students are in the correct lecture, 10 % in the wrong lecture and so on. Now, as described on the process page, we basically just leave away all the variables, and have our transformation matrix A (and hence phi, too).

$$\mathbf A = \frac{1}{10} * \left( \begin{array}{cccc}7 & 2 & ... ...1 & 1 & 1\\ 2 & 4 & 4 & 1\\ 0 & 3 & 4 & 1 \end{array} \right)$$