WBJEE 2012 Math Solved Paper

The system of equations are
x+3y+5z=αx
5x+y+3z=αy
3x+5y+z=αz
⇒(1−α)x+3y+5z=0 ....(i)
5x+(1−α)y+3z=0....(ii)
3x+5y+(1−α)z=0 ....(iii)
For infinite number of solutions, we must have
|

1−α	3	5
5	1−α	3
3	5	1−α

|=0
C1→C1+C2+C3
Taking (9 -α)common from the first column, we get
⇒(9−α)|

α+2	2
−2	α+4

|=0
⇒(9−α)(α2+6α+8+4)=0
(α−9)(α2+6α+12)=0
⇒α=9 is the only real value of a.