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Question
Evaluate the following determinant:
\[\begin{vmatrix}67 & 19 & 21 \\ 39 & 13 & 14 \\ 81 & 24 & 26\end{vmatrix}\]
Solution
\[ ∆ = \begin{vmatrix}67 & 19 & 21 \\ 39 & 13 & 14 \\ 81 & 24 & 26\end{vmatrix}\]
\[ = 67\left( 338 - 336 \right) - 19\left( 1014 - 1134 \right) + 21\left( 936 - 1053 \right)\]
\[ = 67(2) - 19( - 120) + 21( - 117)\]
\[ = 134 + 2280 - 2457\]
\[ = - 43\]
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