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

Step-by-step solution

aligned & [ array ccc 1 & -1 & 1 2 & 1 & -3 1 & 2 & 1 array ] [ array l x y z array ]= [ array l 4 0 2 array ] & R ₃ R ₃- R ₁ and R ₂ R ₂-2 R ₁ & [ array ccc 1 & -1 & 1 0 & 3 & -5 0 & 2 & 0 array ] [ array l x y z array ]= [ array c 4 -8 -2 array ] aligned array lll & y=-1 & [ from (3)] & -3-5 z=-8 z=1 & [ from (2)] & x-(-1)+1=4 x=2 & [ from (1)] & 2 x+y-z=2(2)-1-1=2 & array