Question

Calcule o determinante aplicando a regra de sarrus:

c) [-2 1 3]
__[4 -3 1]
__[2 4 1 ]

Answer 1

|-2 1 3|

|4 -3 1| =

|2 4 1|

=(-2)(-3).1+1.1.2+3.4.4.-[3. (-3).2)+1.2.1+(-2).4.1]=6+2+48-(-18+4-8)=56-(-22)=78

Answer 2

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$\mathbb{P}=\begin{vmatrix}\sf-2&\sf-1&\sf3\\\sf4&\sf-3&\sf1\\\sf2&\sf4&\sf1\end{vmatrix}\begin{vmatrix}\sf-2&\sf-1\\\sf4&\sf-3\\\sf2&\sf4\end{vmatrix}\\\sf det~\mathbb{P}=(-2)\cdot(-3)\cdot1+(-1)\cdot1\cdot2+3\cdot4\cdot4-(-1)\cdot4\cdot1-(-2)\cdot1\cdot4-3\cdot(-3)\cdot2\\\sf det~\mathbb{P}=6-2+48+4+8+18\\\sf det~\mathbb{P}=84-2\\\huge\boxed{\boxed{\boxed{\boxed{\sf det~\mathbb{P}=82}}}}$