The value of a for which system of equation , `a^3x+(a+1)^3y+(a+2)^3z=0, ax+(a+1)y+(a+2)z=0, x+y+z=0,` has a non-zero solution is:

Options

A. 1
B. `0`
C. `-1`
D. None of these

Answer

C

Explanation

For zero solution
`|(a^(3),(a+1)^(3),(a+2)^(3)),(a,(a+1),(a+2)),(1,1,1)|=0`
`implies -|(1,1,1),(a,(a+1),(a+2)),(a^(3),(a+1)^(3),(a+2)^(3))|=0 [ :' R_(1)hArrR_(3)]`
`implies|(1,0,0),(a,1,2),(a^(3),(a+1)^(3)-a^(3),(a+2)^(3)-a^(3))|=0`
`implies |(1,0,0),(a,1,2),(a^(3),1[(a+1)^(2)+a^(2)+a(a+1)],2[((a+2)^(2)+a^(2)),(+a(a+2))])|=0`
`implies|(1,0,0),(a,a,2),(a^(3),(3a^(2)+3a+1),2(3a^(2)+6a+4))|=0`
`implies [6a^(2)+12a+8-(6a^(2)+6a+2)]=0`
`6a+6=0`
`impliesa=-1`