Question

Evaluate the determinant :$\left|\begin{array}{ccc}2& 3& 7\\ 13& 17& 5\\ 15& 20& 12\end{array}\right|$

Answer 1

$\left|\begin{array}{ccc}2& 3& 7\\ 3& 7& 5\\ 5& 0& 2\end{array}\right|$

Expanding along the first row, we get

$=2\left(14\right)-3(6-25)+7(-35)$

$=28+57-245$

$=-160$