If A= [ array ccc 1 & -1 & 1 2 & -1 & 0 3 & 3 & -4 array ], B= [ array l 1 1 2 array ] and X= [ array l x₁ x₂ x₃ array ] such that A X=B , then the value of x₁+x₂+x₃=

Step-by-step solution

aligned & [ array ccc 1 & -1 & 1 2 & -1 & 0 3 & 3 & -4 array ] [ array l x ₁ x ₂ x ₃ array ]= [ array l 1 1 2 array ] & R ₃ R ₃-3 R ₁ and R ₂ R ₂-2 R ₁ & [ array ccc 1 & -1 & 1 0 & 1 & -2 0 & 6 & -7 array ] [ array l x ₁ x ₂ x ₃ array ]= [ array c 1 -1 -1 array ] & R ₃ R ₃-6 R ₂ & [ array ccc 1 & -1 & 1 0 & 1 & -2 0 & 0 & 5 array ] [ array l x ₁ x ₂ x ₃ array ]= [ array c 1 -1 5 array ] & x ₁- x ₂+ x ₃=1 & x ₂-2 x ₃=-1 & 5 x ₃=5 & x ₃=1, x ₂=1, x ₁=1 aligned