any hint ?

Could anyone give me the hint to solve this problem ?

Re: any hint ?

Posted by

me 27 Mar 2011 22:07

Tools of linear algebra work with any field ( https://secure.wikimedia.org/wikipedia/en/wiki/Field_(mathematics) ), including finite ones like integers mod 3. The problem is effectively Gaussian Elimination.

Re: any hint ?

Posted by

sklyack 29 Mar 2011 00:50

But we can't do transformations with antiequations such as with equations. For example, let we have a system:

x1 != 0 (mod 3)

x2 != 2 (mod 3).

It has a solution (2; 0)

If we add the antiequations, we'll get this one:

x1+x2 != 2 (mod 3), but it's wrong for solution (2; 0) of the system!

Am I right?

*Edited by author 29.03.2011 00:53*

Re: any hint ?

Posted by

me 29 Mar 2011 13:45

Uhm, sorry. I was wrong.

Re: any hint ?

Posted by

svr 29 Mar 2011 20:13

I think that your advice is absolutely right!

Let for example det(Aij)<>0.

Then Answer is 2^k,because (A*X)i in {0,1,2}\{bi}

If det(Aij)==0

we can use gauss method to make standard worm of the matrix A.