Question

The value of $\left|\begin{array}{ccc}{1}^2& 2^2& 3^2\\ 2^2& 3^2& 4^2\\ 3^2& 4^2& 5^2\end{array}\right|$ is

• A. -8
• B. 8
• C. 400
• D. 1

Answer 1

The correct option is A -8

$\left|\begin{array}{ccc}{1}^2& 2^2& 3^2\\ 2^2& 3^2& 4^2\\ 3^2& 4^2& 5^2\end{array}\right|\{Operate{R}_3\to R_3-R_2,R_2\to R_2-R_1\}=\left|\begin{array}{ccc}1& 4& 9\\ 3& 5& 7\\ 5& 7& 9\end{array}\right|=1(45-49)-4(27-35)+9(21-25)=-4+32-36=-8.$