If AX = B , where A = [ array ccc 1 & -1 & 1 2 & -1 & 0 3 & 3 & -4 array ], B = [ array l 1 1 2 array ] and X = [ array l x y z array ] , then x+y+z=

Step-by-step solution

Given A= [ array ccc 1 & -1 & 1 2 & -1 & 0 3 & 3 & -4 array ] and B= [ array l 1 1 2 array ], X= [ array l x y z array ] and A X=B AA ⁻¹ X = A ⁻¹ ~B IX = A ⁻¹ ~B X = A ⁻¹ ~B Now | A |=4+(-8)+9=5 aligned A⁻¹ &= [ array lll 4 & -1 & 1 8 & -7 & 2 9 & -6 & 1 array ] 1 5 [ array l x y z array ] &= 1 5 [ array ccc 4 & -1 & 1 8 & -7 & 2 9 & -6 & 1 array ] [ array l 1 1 2 array ] &= 1 5 [ array ll 8-1+2 8-7+4 9-6+2 array ]= 1 5 [ array l 5 5 5 array ] y &= [ array l 1 1 1 array ] aligned On comparing both side, we get x=y=