Let the homogeneous system of linear equations px+y+z=0, x+qy+z=0,x+y+rz=0wherep,q,r≠1have a non-trivial solution then 11−p+11−q+11−r=

The system has a non-trivial solution⇒p111q111r=0apply R1→R1-R3, R2→R2-R3 ⇒p-101-r0q-11-r11r=0 ⇒p-1q-1r-11-r-0+1-r0-1q-1=0 ⇒1-p1-qr+1-p1-r+1-q1-r=0 Dividing throughout by 1-p1-q1-r, we get          r1-r+11-q+11-p=0     ⇒ r-1+11-r+11-q+11-p=0     ⇒11-p+11-q+11-r=1