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

Answer

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

Explanation

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

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

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