Solve the equation.
\(\begin{pmatrix} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & -1 & -1 \end{pmatrix}\begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 1 \\ -1 \\ 1 \end{pmatrix}\)
x + y = 1 ⇒ x - 1 = - y (1)
x + z = -1 ⇒ x + 1 = - z (2)
x - y - z = 1 (3)
Sub (1) and (2) into (3)
x + ( x -1) + ( x + 1) = 1
3x = 1
x =1/3
y = 2/3
z = -4/3