Question

The value of determinant $\left|\begin{array}{ccc}x+1& x+2& x+4\\ x+3& x+5& x+8\\ x+7& x+10& x+14\end{array}\right|$ is?

• A. $-2$
• B. $x^2+2$
• C. $2$
• D. None of these

Answer 1

The correct option is A $-2$

Operating $C_3-C_2$ and $C_2-C_1$, we get $\Delta =\left|\begin{array}{ccc}x+1& 1& 2\\ x+3& 2& 3\\ x+7& 3& 4\end{array}\right|$
Apply $R_3-R_2,R_2-R_1$
$\Delta =\left|\begin{array}{ccc}x+1& 1& 2\\ 2& 1& 1\\ 4& 1& 1\end{array}\right|$ apply $C_3-C_2$
$\left|\begin{array}{ccc}x+1& 1& 1\\ 2& 1& 0\\ 4& 1& 0\end{array}\right|=1.(2-4)=-2$