For the system x-y+z=4,2 x+y-3 z=0 , x+y+z=2 , the values of x, y, z respectively are given by

Step-by-step solution

Given equation in matrix form [ array ccc 1 & -1 & 1 2 & 1 & -3 1 & 1 & 1 array ] [ array l x y z array ]= [ array l 4 0 2 array ] It is of the form AX = B Now, |A|= | array ccc 1 & -1 & 1 2 & 1 & -3 1 & 1 & 1 array |=10 0 aligned & A⁻¹ exist & adj A= [ array ccc 4 & 2 & 2 -5 & 0 & 5 1 & -2 & 3 array ] A⁻¹ & = 1 |A| adj A & = 1 10 [ array ccc 4 & 2 & 2 -5 & 0 & 5 1 & -2 & 3 array ] aligned array ll & Now, A X=B & A⁻¹(A X)=A⁻¹ B & X=A⁻¹ B array aligned X & = 1 10 [ array ccc 4 & 2 & 2 -5 & 0 & 5 1 & -2 & 3 array ] [