find the invese of the matraix `[(1,2,5),(2,3,1),(-1,1,1)],` using elementary row operaations.

find the invese of the matraix `[(1,2,5),(2,3,1),(-1,1,1)],` using ele

1.	find the invese of the matraix `[(1,2,5),(2,3,1),(-1,1,1)],` using elementary row operaations.
Answer» Let `A=[(1,2,5),(2,3,1),(-1,1,1)],` `therefore" " \|A\|=[(1,2,5),(2,3,1),(-1,1,1)],=1(3-1)-2(2+1)+5(2+3)=21!=0` `therefore" " A^(-1)` exists. We write A=IA `rArr" " [(1,2,5),(2,3,1),(-1,1,1)]=[(1,0,0),(0,1,0),(-0,0,1)]` Applying `R_(2) to R_(2)` and `R_(3) to R_(3) +R_(1),` we get ` [(1,2,5),(0,-1,-9),(0,3,6)]=[(1,0,0),(-2,1,0),(1,0,1)]A` Applying `R_(2) to (-1)R_(2)` and `R_(3) to ((1)/(3))R_(3),` we get ` [(1,2,5),(0,1,9),(0,1,2)]=[(1,0,0),(2,-1,0),((1)/(3),0,(1)/(3))]A` Applying `R_(1) to R_(1)-2R_(2)` and `R_(3)to R_(3)-R_(2),` we get ` [(1,0,-13),(0,1,9),(0,0,-7)]=[(-3,2,0),(2,-1,0),((-5)/(3),1,(1)/(3))]A` Applying `R_(3) to (-(1)/(7))` we get ` [(1,0,-13),(0,1,9),(0,0,1)]=[(-3,2,0),(2,-1,0),((-5)/(21),-(1)/(7),(1)/(21))]A` Applying `R_(2) to R_(2)-9R_(3)` and `R_(1) to R_(1) +13R_(3),` we get ` [(1,0,0),(0,1,0),(0,0,1)]=[((2)/(21),(1)/(7),-(13)/(21)),(-(1)/(7),(2)/(7),(3)/(7)),((5)/(21),-(1)/(7),-(1)/(21))]A` Hence `A^(-1)=[((2)/(21),(1)/(7),-(13)/(21)),(-(1)/(7),(2)/(7),(3)/(7)),((5)/(21),-(1)/(7),-(1)/(21))]`

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find the invese of the matraix `[(1,2,5),(2,3,1),(-1,1,1)],` using elementary row operaations.

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