Evaluate the determinant. $\left| \begin{array} { l l l }
1 & 0 & 1 \
0 & 1 & 0 \
1 & 1 & 1
\end{array} \right|$
A) 0
B) -2
C) 2
D) -1
E) 1

Question

Evaluate the determinant. $\left| \begin{array} { l l l } 
1 & 0 & 1 \
0 & 1 & 0 \
1 & 1 & 1
\end{array} \right|$
A) 0
B) -2
C) 2
D) -1
E) 1

Quizplus · Accepted Answer

We can expand the determinant using the first row or the second row. If we use the first row, we get:
\begin{align*}
\left|\begin{array}{lll}
1 & 0 & 1 \
0 & 1 & 0 \
1 & 1 & 1
\end{array}ight| &= 1\cdot\left|\begin{array}{ll}1&0\1&1\end{array}ight| - 0\cdot\left|\begin{array}{ll}0&1\1&1\end{array}ight| + 1\cdot\left|\begin{array}{ll}0&1\1&0\end{array}ight| \
&= 1\cdot(1) - 0\cdot(-1) + 1\cdot(-1) \
&= \boxed{0}.
\end{align*}

Evaluate the Determinant ∣101010111∣\left| \begin{array} { l l l } 1 & 0 & 1 \\0 & 1 & 0 \\1 & 1 & 1\end{array} \right|​101​011​101​​

Evaluate the Determinant $\left| \begin{array} { l l l } 1 & 0 & 1 \\0 & 1 & 0 \\1 & 1 & 1\end{array} \right|$