Question

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:

• A. \( -1 \)
• B. \( 0 \)
• C. \( 1 \)
• D. \( 2 \)

Hint:

For a homogeneous system \( AX = 0 \) to have a non-trivial solution, the determinant \( |A| \) must be zero.