Question

Evaluate the determinant: $\left|\begin{array}{ccc}38& 7& 63\\ 16& 3& 29\\ 27& 5& 46\end{array}\right|$

Answer 1

Apply $C_{1}5-C_2,C_3-9C_2$ to reduce the numbers

$△=\left|\begin{array}{ccc}3& 7& 0\\ 1& 3& 2\\ 2& 5& 1\end{array}\right|$

Apply $R_2-2R_3$

$△=$ $\left|\begin{array}{ccc}3& 7& 0\\ -3& -7& 0\\ 2& 5& 1\end{array}\right|$ =0.

As $R_1$ and $R_2$ are identical.