$$\left| {\matrix{ 3 & { - 2} & 1 \cr 5 & { - 8} & 9 \cr 2 & 1 & a \cr } } \right| = 0 \Rightarrow - 14a - 42 = 0 \Rightarrow a = - 3$$

Now 3 (equation (1)) $$-$$ (equation (2)) $$-$$ 2 (equation (3)) is

$$3(3x - 2y + z - b) - (5x - 8y + 9z - 3) - 2(2x + y + az + 1) = 0$$

$$ \Rightarrow - 3b + 3 - 2 = 0 \Rightarrow b = {1 \over 3}$$

So for no solution $$a = - 3$$ and $$b \ne {1 \over 3}$$