Examine the consistency of the following system of equation
x+y+z=1
2x +3y+2z =2
ax +ay +2az =4

Explanation

Here A=[[1,1,1],[2,3,2],[a,a,2a]]
`therefore |A|=1 |[3,2],[a,2a]|-1|[2,2],[a,2a]|+1|[2,3],[a,a]|
`=(6a -2a)-(4a-2a)+(2a-3a)
`=4a-2a-a=a!=0`
(Clearly `a!= 0` because if a=0, then the third equation would not exist)`therefore`The given system is consistent