Evaluate the following determinant:
$$ det \left( \begin{matrix}1&0&4&-6\\2&5&0&3\\-1&2&3&5\\2&1&-2&3\end{matrix} \right) $$

Answer

$$ det \left( \begin{matrix}1&0&4&-6\\2&5&0&3\\-1&2&3&5\\2&1&-2&3\end{matrix} \right) = 318 $$

Explanation

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Evaluate the following determinant: $$ det \left( \begin{matrix}1&0&4&-6\\2&5&0&3\\-1&2&3&5\\2&1&-2&3\end{matrix} \right) $$

$$ det \left( \begin{matrix}1&0&4&-6\\2&5&0&3\\-1&2&3&5\\2&1&-2&3\end{matrix} \right) = 318 $$

Evaluate the following determinant:
$$ det \left( \begin{matrix}1&0&4&-6\\2&5&0&3\\-1&2&3&5\\2&1&-2&3\end{matrix} \right) $$