MATH Matrix Equation
posted by per4mer .
If
4a + 3b + c = 27
3a + b + 4c = 16
9a + 2b + 3c = 33
then 2a + 2b + 2c = ?

Why don't you just solve the matrix on your calc, or with row reduction, then add a+b+c?

Or 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:
R2Q = 3a  5c = 1
P3Q = 5a  11c = 21
so
5(R2Q) = 15a  25c = 5
3(P3Q) = 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. 
Correction: 58c=58, so c=1.