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August 24, 2016
Posted by **per4mer** on Monday, September 22, 2008 at 7:30pm.

4a + 3b + c = 27

3a + b + 4c = 16

9a + 2b + 3c = 33

then 2a + 2b + 2c = ?

- MATH Matrix Equation -
**bobpursley**, Monday, September 22, 2008 at 7:45pmWhy don't you just solve the matrix on your calc, or with row reduction, then add a+b+c?

- MATH Matrix Equation -
**David Q**, Tuesday, September 23, 2008 at 2:59pmOr to get it algebraically, call the equations P, Q and R respectively, so

P: 4a + 3b + c = 27

Q: 3a + b + 4c = 16

R: 9a + 2b + 3c = 33

Solve these for b first, since the multiples are easy:

R-2Q = 3a - 5c = 1

P-3Q = -5a - 11c = -21

so

5(R-2Q) = 15a - 25c = 5

3(P-3Q) = -15a - 33c = -63

Add these together and you get -58c = 58, so c=1, therefore a=2. Feed a and c into any of the original equations and you get b=6. So a+b+c=9, and twice this is 18. - MATH Matrix Equation -
**David Q**, Tuesday, September 23, 2008 at 3:02pmCorrection: -58c=-58, so c=1.