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Cache of mathematical awesomeness Mystery Cache

Hidden : 3/22/2010
Difficulty:
3 out of 5
Terrain:
1.5 out of 5

Size: Size:   small (small)

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Geocache Description:

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48w + 376x + 19y + 203z = 213042

203w + 48x + 376y + 19z = 41020

19w - 203x + 48y - 376z = -202392

376w - 48x + 203y - 19z = -2806

This will give you N45° w.x and W119° y.z


Solve this Algebra-inspired puzzle to gain the coordinates of a quick, easy hide.

You'll have to have a strong understanding of linear algebra to solve this. This can be done by hand but use of a graphing calculator or computer might help. This puzzle will rely on solving systems of linear equations (which you can Google for help.) Using a matrix to solve this puzzle might simplify it considerably.

Here are some time lines you might want to consider;

A) web based rref matrix calculator http://www.math.purdue.edu/~dvb/matrix.html "5 minutes"

B) TI graphing calculator using matrix function. Directions: fill in matrix, select rref (your matrix name), read the row reduced answer "15 minutes"

C) Linear combination or Substitution using long hand. Refer to high school math text:) "45+ minutes"

You can check your answers for this puzzle on Geochecker.com.

Additional Hints (No hints available.)