I'm assuming that

| 0 2 |

| 0 0 |

is a coefficient matrix A for some

AX=C, where

X = [x y]^T (X is the column vector of variables)

C = [a b] (C is just some column vector of constants)

In that case x does not equal 0. In fact, x is not even in the system of equations since its coefficients are all 0's anyways.

Rewritten in the form of equations, your matrix translates to:

0x + 2y = a

0x + 0y = b

So if b does not equal 0, then there is no solution to the matrix

also y = a/2 for all possible values of a

x can be anything.