If `A=[(1,2,-3),(2,3,2),(3,-3,-4)]` then find `A^-1` and hence solve the follwoing equations: `x+2y-3z=4, 2x+3y+2z=2 and 3x-3y-4z=11`

Explanation

We have given

`A=[(1,2,-3),(2,3,2),(3,-3,-4)]`

Determinant of matrix A,

`∣A∣=|(1,2,-3),(2,3,2),(3,-3,-4)|`

`∣A∣=1(-12+6)-2(-8-6)-3(-6-9)=67ne0`

So, `A^(−1)`exists.

To find adjoint of matrix A we first find cofactors

`C_(11)=-6,C_(12)=14,C_(13)=-15,C_(21)=17,C_(22)=5,C_(23)=9,C_(31)=13,C_(32)=-8,C_(33)=-1`

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