If p $$\ne$$ a, q $$\ne$$ b, r $$\ne$$ c and the system of equations

px + ay + az = 0

bx + qy + bz = 0

cx + cy + rz = 0

has a non-trivial solution, then the value of $$\frac{p}{p-a}+\frac{q}{q-b}+\frac{r}{r-c}$$ is

Matrix $$A = \left| {\matrix{ x & 3 & 2 \cr 1 & y & 4 \cr 2 & 2 & z \cr } } \right|$$, if xyz = 60 and 8x + 4y + 3z = 20, then A(adj A) is equal to

An ordered pair ($$\alpha$$, $$\beta$$) for which the system of linear $$(1 + \alpha )x + \beta y + z = 2$$, $$\alpha x + (1 + \beta )y + z = 3$$, $$\alpha x + \beta y + 2z = 2$$ has a unique solution.