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 B $-8$

$△=\left|\begin{array}{ccc}{1}^2& 2^2& 3^2\\ 2^2& 3^2& 4^2\\ 3^2& 4^2& 5^2\end{array}\right|$
$△=\left|\begin{array}{ccc}1& 4& 9\\ 4& 9& 16\\ 9& 16& 25\end{array}\right|$
$C_3\to C_3-C_2,C_2\to C_2-C_1$
$△=\left|\begin{array}{ccc}1& 3& 5\\ 4& 5& 7\\ 9& 7& 9\end{array}\right|$
$C_3\to C_3-C_2,C_2\to C_2-C_1$
$△=\left|\begin{array}{ccc}1& 2& 2\\ 4& 1& 2\\ 9& -2& 2\end{array}\right|$
$R_3\to R_3-R_2,R_2\to R_2-R_1$
$△=\left|\begin{array}{ccc}1& 2& 2\\ 3& -1& 0\\ 5& -3& 0\end{array}\right|$
$=2(-9+5)=-8$