If A X=D represents the system of simultaneous linear equations x+y+z=6 , 5 x-y+2 z=3 and 2 x+y-z=-5 , then ( Adj A) D=

Step-by-step solution

The given system of equation is 5 x-y+2 z=3, x+y+z=6 and 2 x+y-z=-5 In matrix form, if may be represented as where A= [ array ccc 1 & 1 & 1 5 & -1 & 2 2 & 1 & -1 array ], x= [ array l x y z array ] and D= [ array c 6 3 -5 array ] Thus, A is a non-singular matrix, so A⁻¹ exist. aligned & C₁₁=(-1)¹⁺¹ | array cc -1 & 2 1 & -1 array |=-1 & C₁₂=(-1)¹⁺² | array cc 5 & 2 2 & -1 array |=9 & C₁₃=(-1)¹⁺³ | array cc 5 & -1 2 & 1 array |=7 & C₂₁=(-1)²⁺¹ | array cc 1 & 1 1 & -1 array |=2 aligned aligned & C₂₂=(-1)²⁺² | array ll