If `A=[(1,2, 1), (-1, 1,1), (1, -3, 1)],` find `A^(-1)` and hence solve the system of linear equation. `x+2y+z=4,-x+y+z=0,x-3y+z=2`

Explanation

We have given

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

Determinant of matrix A,

∣A∣`=|(1,2, 1), (-1, 1,1), (1, -3, 1)|`

`∣A∣=1(1+3)-2(-1-1)+1(3-1)=10ne0`

So, `A^(−1)`exists.

To find adjoint of matrix A we first find cofactors

`C_(11)=4,C_(12)=2,C_(13)=2,C_(21)=-5,C_(22)=0,C_(23)=5,C_(31)=1,C_(32)=-2,C_(33)=3`

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