If pqr≠0 and the system of equations(p+a)x+by+cz=0ax+(q+b)y+cz=0ax+by+(r+c)z=0has a non-trivial solution, then value of ap+bq+cr is

Δ=p+abcaq+bcabr+c=0Applying R2→R2−R1 and R3→R3−R1, we getp+abc−pq0−p0r=0or   pqc + [q(p + a) + bp]r = 0Dividing by pqr, we obtainap+bq+cr=−1