Question

(Determinantes) Calcule

$\left[\begin{array}{ccc}-1&4&5\\-2&1&0\\-3&2&7\end{array}\right]$

Answer 1

$\left|\begin{matrix}-1&4&5\\-2&1&0\\-3&2&7\end{matrix}\right|=(-1)^{1+3}\cdot 5\left|\begin{matrix}-2&1\\-3&2\end{matrix}\right|+(-1)^{3+3}\cdot 7\left|\begin{matrix}-1&4\\-2&1\end{matrix}\right| \\ \\ \\ \left|\begin{matrix}-1&4&5\\-2&1&0\\-3&2&7\end{matrix}\right|=5[(-2)(2)-(1)(-3)]+7[(-1)(1)-(-2)(4)]\\ \\ \\ \left|\begin{matrix}-1&4&5\\-2&1&0\\-3&2&7\end{matrix}\right|=5[-1]+7[7]\\ \\ \\ \left|\begin{matrix}-1&4&5\\-2&1&0\\-3&2&7\end{matrix}\right|=44$