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Question
Evaluate the following determinant:
\[\begin{vmatrix}1 & 4 & 9 \\ 4 & 9 & 16 \\ 9 & 16 & 25\end{vmatrix}\]
Solution
\[ ∆ = \begin{vmatrix}1 & 4 & 9 \\ 4 & 9 & 16 \\ 9 & 16 & 25\end{vmatrix}\]
\[ = 1\begin{vmatrix}9 & 16 \\ 16 & 25\end{vmatrix} - 4\begin{vmatrix}4 & 16 \\ 9 & 25\end{vmatrix} + 9\begin{vmatrix}4 & 9 \\ 9 & 16\end{vmatrix}\]
\[ = 1\left( 225 - 256 \right) - 4\left( 100 - 144 \right) + 9\left( 64 - 81 \right)\]
\[ = 1( - 31) - 4( - 44) + 9( - 17)\]
\[ = - 31 + 176 - 153\]
\[ = - 8\]
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