If the solution for the system of equations x+2 y-z=3 , 3 x-y+2 z=1 and 2 x-2 y+3 z=2 is ( , , ) , then ^2+ ^2+ ^2=

Step-by-step solution

[ array ccc 1 & 2 & -1 3 & -1 & 2 2 & -2 & 3 array ] [ array l x y z array ]= [ array l 3 1 2 array ] Augmented matrix is: aligned & [ array ccccc 1 & 2 & -1 & : & 3 3 & -1 & 2 & : & 1 2 & -2 & 3 & : & 2 array ] & R₂ R₂-3 R₁ & R₃ R₃-2 R₁ & [ array ccccc 1 & 2 & -1 & : & 3 0 & -7 & 5 & : & -8 0 & -6 & 5 & : & -4 array ] & R₃ 7 R₃-6 R₂ & [ array ccccc 1 & 2 & -1 & : & 3 0 & -7 & 5 & : & -8 0 & 0 & 5 & : & 20 array ] aligned Rank (A: B)= Rank (A)=3 Solution exists and can be given by : aligned & [ array ccc 1 & 2 & -1