Most of you have probably seen matrix multiplication in action. If you've ever played a 3-D computer game or seen a movie with computer animation (like "The Matrix" for instance), you've probably seen the results of some pretty intense matrix multiplication since the technique is a very convenient method for managing transformations of coordinate systems... hmmm, coordinate systems. Now there's something that sounds famailiar.
This puzzle requires you to learn some basic matrix/vector multiplication (not here - try a google or wikipedia search) so you can transform the listed coordinates into a new set of coordinates that will lead you to a one lane bridge. There is space to park on the South side of the bridge. On the bridge you will find a 3-digit number that the same matrices will transform into the final North and West coordinates. You can reach the final location on foot via a short hike on a trail along the creek. Cache is a small tupperware container sandwiched between thorns and a large solid square... Watch out for poison ivy along either side of the trail.
Here are the matrices:
All three digit numbers should be treated as a 3-dimensional column vector where each digit represents a dimension.
1. To find the first set of coordinates (the bridge), the last 3 digits of the listed North and West coordinates must both be transformed using the corresponding North and West matrices into a new set of 3 digit numbers. These will be the actual coordinates for the bridge.
2. The final coordinates will have to be computed in the field, so make sure you know what you're doing! Once you've found the 3-digit number on the bridge, multiply that 3-digit number by N to get the final North coordinate, and multiply the number by W to get the final West coordinate. Then go for a walk on a trail.
Don't bother trying to flush yourself out of the Matrix at the final. It won't work unless you take the red pill.
You can check your solution
here.