Let A= [ array ccc 1 & -1 & 1 2 & 1 & -3 1 & 1 & 1 array ] and B= [ array l 4 0 2 array ] such that AX = B , then X =

Step-by-step solution

aligned & AX = B & [ array ccc 1 & -1 & 1 2 & 1 & -3 1 & 1 & 1 array ] [ array l x₁ x₂ x₃ array ]= [ array l 4 0 2 array ] aligned Applying R ₂ R ₂-2 R ₁ and R ₃ R ₃- R ₁ , [ array ccc 1 & -1 & 1 0 & 3 & -5 0 & 2 & 0 array ] [ array l x₁ x₂ x₃ array ]= [ array c 4 -8 -2 array ] array ll & x₁-x₂+x₃=4 ...(i) & 3 x₂-5 x₃=-8 ...(ii) & 2 x₂=-2 x₂=-1 array From (ii), 3(-1)-5 x₃=-8 x₃=1 From (i), aligned & x₁+1+1=4 x₁=2 & [ array l x₁ x₂ x₃ array ]= [ array c 2 -1 1 array ] aligned