by nsguy1350 » Wed Feb 29, 2012 7:52 pm
Ok, notice that [(1,0)(0,1)] is an identity matrix. I think that you can just find the inverse of the first matrix (A) to find out.
If you have a TI-89, enter: [-1,-2;3,4]^(-1) to find the inverse.
If you have an 83/84, I think you enter the matrix in the matrix menu, then either use the inverse function if there is one, or put it to the -1.
Did you mean 12ab in the second one? Then, you could factor that into [unparseable or potentially dangerous latex formula]. Square rooting both sides gives [unparseable or potentially dangerous latex formula], so [unparseable or potentially dangerous latex formula],
so [unparseable or potentially dangerous latex formula].
Ok, well, you go through 7 years from 2004 to 2011. The only leap day between Christmas 2004 and 2011 occurs in 2008 (The leap year had already passed in 2004).
This means you go through 7x365 + 1 days. Modding 7x365 + 1 by 7 is easy, since the 7x365 will give 0, and the 1 is just 1. You advance one day from Saturday to Sunday, so your final answer is Sunday.
By the "3rd" I believe he is referring to March 3, a Saturday where we are having our next competition.
2013 District 1/Region:
NS - 319/355
MA - 340/332
CA - 294/287
SC - 344/292
CS - 212/124 (fail)