System of equation over GF(211) (corrected) I have this system of equation.
$a+b+c=171, a+2b+4c = 46, a+3b+9c = 170$.
My task is to solve this system over $GF(211)$.
Is there any special process?
Thanks for advice.
 A: There is no such thing as $GF(221)$; finite fields exist only for prime-power orders; $221=13\cdot17$.
A: To answer your question "is there a special process", the answer is it depends on the underlying (field) number system. Processes like gaussian elimination always work but gram-schmidt and hence any method based on it doesn't always work even if a unique solution exists. For example in a vector space over a binary field gram-schmidt doesn't work because you can have a nonzero vector which is orthogonal to all other vectors. In real/complex fields the zero vector is the only one with this property.
The general rule to remember, in whatever number system you are working in, if the determinant of the matrix is invertible then the matrix itself is invertible. And if it is invertible then it will have a unique inverse and hence your system will have a unique solution. If the determinant isn't invertible then you can problems like no solutions or more than one (finite or infinite).
In this case, did you mean the ring Z/221Z or the field Z/223Z? In either case the determinant of your matrix is 2 which is invertible in both because 2 is coprime to both 221 and 223. So I would just use any standard method. The only thing to remember is that the arithmetic would be in whatever number system you are using.
