Answer
-2
Work Step by Step
First, use cofactor expansion (Theorem 4.1) along the first row:
\[
\begin{vmatrix}
1 & 1 & 0\\1 & 0 & 1\\0 & 1 & 1
\end{vmatrix}
=
1 \cdot
\begin{vmatrix}
0 & 1\\1 & 1
\end{vmatrix}
-1 \cdot
\begin{vmatrix}
1 & 1\\0 & 1
\end{vmatrix}
+0
\]
Then, simplify the expansion:
$=1 \cdot (0-1) - 1 \cdot (1-0)$
$=-1-1$
$=-2$
