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

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SOLUTION :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


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