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Default Using Macros to Calculate Matrix Algebra in Excel..... I'm STUMPED

Hello!
Here is a link to a file with my situation:

http://www.savefile.com/files/8301241

I need to find a way to set up a spreadsheet where I can input the variables
G, H, W, J, Q, S and have excel calculate the possible answers that satisfy
all of the equations in column D.

I know to do this on paper you use matrix algebra but I have no clue how to
do this in excel.

Column B is the results I should be getting for each variable in column A
(with the input values in column F) but I can't get it to work in excel.
Column C is a quick attempt I made to use iterate and circular references but
to no avail. If anyone can point me in the right direction I would REALLY
appreciate it. Oh and column A is a list of all variables used in the
equations in column D.

Is it even possible to input values for the variables in column E and have
excel use those to find answers that satisfy all of the equations in column
D??

 
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