Question

Evaluate the following determinant:

\[\begin{vmatrix}1 & 3 & 5 \\ 2 & 6 & 10 \\ 31 & 11 & 38\end{vmatrix}\]

Answer 1

\[ ∆ = \begin{vmatrix}1 & 3 & 5 \\ 2 & 6 & 10 \\ 31 & 11 & 38\end{vmatrix}\]
\[ = 1 \begin{vmatrix}6 & 10 \\ 11 & 38\end{vmatrix} - 3\begin{vmatrix}2 & 10 \\ 31 & 38\end{vmatrix} + 5\begin{vmatrix}2 & 6 \\ 31 & 11\end{vmatrix}\]
\[ = 1\left( 228 - 110 \right) - 3\left( 76 - 310 \right) + 5\left( 22 - 186 \right)\]
\[ = 1(118) - 3( - 234) + 5( - 164)\]
\[ = 118 + 702 - 820\]
\[ = 0\]