Question

The determinant $\left|\begin{array}{ccc}1& 1& 1\\ 1& 2& 3\\ 1& 3& 6\end{array}\right|$ is not equal to

• A. $\left|\begin{array}{ccc}2& 1& 1\\ 2& 2& 3\\ 2& 3& 6\end{array}\right|$
• B. $\left|\begin{array}{ccc}2& 1& 1\\ 3& 2& 3\\ 4& 3& 6\end{array}\right|$
• C. $\left|\begin{array}{ccc}1& 2& 1\\ 1& 5& 3\\ 1& 9& 6\end{array}\right|$
• D. $\left|\begin{array}{ccc}3& 1& 1\\ 6& 2& 3\\ 10& 3& 6\end{array}\right|$

Answer 1

The correct option is A $\left|\begin{array}{ccc}2& 1& 1\\ 2& 2& 3\\ 2& 3& 6\end{array}\right|$

$\left|\begin{array}{ccc}1& 1& 1\\ 1& 2& 3\\ 1& 3& 6\end{array}\right|=\left|\begin{array}{ccc}2& 1& 1\\ 3& 2& 3\\ 4& 3& 6\end{array}\right|by{C}_1\to C_1+C_2\left|\begin{array}{ccc}1& 2& 1\\ 1& 5& 3\\ 1& 9& 6\end{array}\right|by{C}_2\to C_2+C_3\left|\begin{array}{ccc}3& 1& 1\\ 6& 2& 3\\ 10& 3& 6\end{array}\right|,by{C}_1\to C_1+C_2+C_3.But\ne \left|\begin{array}{ccc}2& 1& 1\\ 2& 2& 3\\ 2& 3& 6\end{array}\right|$.