Martrices dilemma

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
1) Do NOT post problems in Microsoft Word attachements. They are notorious for viruses and many people will not open them. Also, since the federal government forced Microsoft to stop "bundling" Word with Windows, many people do not have "Word".

2) There are two ways to get the "One stop over" matrix.

Directly from the given map: start at any city and see which you can go between in two steps: From Boussain, you can get to Boussain by first going to Brandon. So there is a "1" in the "Bo","Bo" cell. From Boussain you can go to Brandon by going through Killarney. So there is a "1" in the "Bo","Br" cell. From Boussain you can go to Virden by going through Brandon. So there is a "1" in the "Bo","Vi" cell. That's the first row. The second row corresponds to Brandon. From Brandon you can go to Virden and then to Melita so there is a "1" in the "Br","M" cell. If, instead of going to Virden, you first go to Boussain, you can then go to Killarney so there is a "1" in the "Br","K" cell. But if you first go to Boussain, you can go back to Brandon so there is a "1" in the "Br","Br" cell. Get the idea?

But the less "basic", more "algebraic" thing to do is to square the matrix- multiply it by itself. Since the matrix corresponds to "you can go from A to B", the squared matrix corresponds to "you can go from A to B to C", one stopover.
 
Last edited:
Jul 2010
85
0
thank you

great explanations. They've really helped me to understand the problem. Thanks again