Suppose \( p, q, r \neq 0 \) and the system of equations:
\[
(p + a)x + by + cz = 0
\]
\[
ax + (q + b)y + cz = 0
\]
\[
ax + by + (r + c)z = 0
\]
has a non-trivial solution, then the value of
\[
\frac{a}{p} + \frac{b}{q} + \frac{c}{r}
\]
is:
Show Hint
For a homogeneous system \( AX = 0 \) to have a non-trivial solution, the determinant \( |A| \) must be zero.