Glover Problem B Part 2

Once again, we will use the file ``basefile.m''. The second file that we use in this step is nearly identical to the one we used in part 1 of problem B. The file is called problem2.step2.m. The only difference between this file and problem2.m, which we used in step 1 is the additional relations which set P13 and its transpose P31 to zero.

In this step the NCProcess command creates a spreadsheet file called ``Banswer2.dvi''. Once again we have quite a few more relations than we actually care to look at. All that we need to do is find some categories which allow us to make some progress. As long as we can gain some additional knowledge, we can feed it back into the computer and let the computer do the work.

It turns out that there are at least three interesting categories in this spreadsheet. The first one tells us something about P33.

The expressions with unknown variables

and knowns

The first equations tells us that P33 acts like 2 on the range of B2. The remaining equations in this category give many independent constraints satisfied by P33 equals 2. This motivates the assumption that P33 is, in fact, 2 times the identity matrix.

The following category is very similar. By the same analysis we can assume that that the inverse of P33 is 1/2 times the identity. This also supports our assumption about P33 itself.

The expressions with unknown variables

and knowns

Using our assumtion about P33, the following category allows us to solve for P23.

The expressions with unknown variables

and knowns

If we manually substitute for P33, we can see that P23 is zero. This category is analogious to the category in step 1 that allowed us to assume P13 was zero. At this point we could analyze the spreadsheet further, but since we have made significant progress we will make the assumptions that we have noted here and move on to step 3.