If A X=B , where A= [ array lll 1 & 3 & 3 1 & 4 & 4 1 & 3 & 4 array ], X= [ array l x y z array ] and B= [ array l 12 15 13 array ] , then x²+y²+z²=

Step-by-step solution

(A) Given AX = B [ array lll 1 & 3 & 3 1 & 4 & 4 1 & 3 & 4 array ] [ array l x y z array ]= [ array c 12 15 13 array ] R ₂ R ₂- R ₁ and R ₃ R ₃- R ₁ [ array lll 1 & 3 & 3 0 & 1 & 1 0 & 0 & 1 array ] [ array l x y z array ]= [ array l 12 3 1 array ] [ array l x+3 y+3 z y+z z array ]= [ array l 12 3 1 array ] aligned & x+3 y+3 z=12 & y+z=3 & z=1 aligned Thus z=1, y=2, x=3 x²+y²+z²=9+4+1=14