Exercise 5 8 5 Draw 5 dots on a piece of paper and label them po P1 P2 P3 P4 Decide to connect some of these dots and not others Now make a matrix which has the same number of columns as there are dots and the same number of rows as there are connections you drew Label the rows for the connections like 01 03 14 etc Now for each connection you make from p to p in order so that i j for example if you connect p4 and po we will call this po to p4 in the corresponding row put a 1 in the column for p and a 1 in the column for p and 0 in all other columns Now study the kernel of this matrix Its dimension will equal the number of connected components your picture had For example if all the pieces form one cluster you will have one kernel dimension Try to do this a second time so that your picture has two distinct clusters and see if you can reflect that in your computation of the kernel This is a warm up for one of our final projects