Chapter 9 - Section 9.1 - Solving Systems of Linear Equations in Three Variables and Problem Solving - Exercise Set - Page 641: 51

$[1, 1, -1]$

$x+y+z=1$ $2x-y+z=0$ $-x+2y+2z=-1$ $x+y+z+(-x+2y+2z)=1+(-1)$ $x+y+z-x+2y+2z=0$ $3y+3z=0$ $(3y+3z)/3=0/3$ $y+z=0$ $x+y+z=1$ $x+(y+z)=1$ $y+z=0$ $y+z-y=0-y$ $z=-y$ $x+0=1$ $x=1$ $2x-y+z=0$ $2*1-y+z=0$ $2-y+z=0$ $2-y+(-y)=0$ $2-y-y=0$ $2-2y=0$ $2-2y+2y=0+2y$ $2=2y$ $2/2=2y/2$ $1=y$ $x+y+z=1$ $1+1+z=1$ $2+z=1$ $2+z-2=1-2$ $z=-1$ $[1, 1, -1]$ $x/8 + y/4 + z/3$ $1/8 + 1/4 - 1/3$ $1/8 + 1*2/4*2 - 1/3$ $1/8 + 2/8 - 1/3$ $3/8 - 1/3$ $3*3/8*3 - 1*8/3*8$ $9/24 - 8/24$ $1/24$