Question

Calcule o valor do determinante de:
[3 9 -1]
[0 1 -4]
[1 2 -3]

a) -20
b)20
c) 70
d) -70

Answer 1

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$\tt B=\begin{bmatrix}\sf3&\sf~~9&\sf-1\\\sf0&\sf~~1&\sf-4\\\sf1&\sf~~2&\sf-3\end{bmatrix}\\\sf det~B=3\cdot\begin{bmatrix}\sf1&\sf-4\\\sf2&\sf-3\end{bmatrix}-9\cdot\begin{bmatrix}\sf0&\sf-4\\\sf1&\sf-3\end{bmatrix}-1\cdot\begin{bmatrix}\sf0&\sf1\\\sf1&\sf2\end{bmatrix}\\\sf det~B=3\cdot(1\cdot(-3)-2\cdot(-4))-9\cdot(0\cdot(-3)-1\cdot(-4))-1\cdot(0\cdot2-1\cdot1)\\\sf det~B=3\cdot(-3+8)-9\cdot(0+4)-1\cdot(0-1)\\\sf det~B=15-36+1\\\sf det~B=-20\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~a}}}}$