The Matrix $\left[\begin{array}{rrr}1 / 2 & -1 & 1 / 2 \\1 / 2 & 0 & -1 / 2 \\-1 / 2 & 1 & 1 / 2\end{array}\right]$

Short Answer

The matrix $\left[\begin{array}{rrr}1 / 2 & -1 & 1 / 2 \\1 / 2 & 0 & -1 / 2 \\-1 / 2 & 1 & 1 / 2\end{array}\right]$
is the inverse of
$\left[\begin{array}{lll}1 & 2 & 1 \\0 & 1 & 1 \\1 & 0 & 1\end{array}\right]$
Solve the following system by the
inverse matrix method.
x+2 y+z =10
y+z =6
x+z =-8