Question

calcule o determinante da matriz

Answer 1

Explicação passo-a-passo:

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Temos a seguinte matriz:

$\boxed{A=\left(\begin{array}{ccc}2&3&1\\0&1&-8\\-3&4&1/3 \end{array}\right)}$

Calculando o determinante:

$detA=\left|\begin{array}{ccc}2&3&1\\0&1&-8\\-3&4&1/3 \end{array}\right|\\\\\text{Usando a Regra de Sarrus:}\\\\detA=\left|\begin{array}{ccc}2&3&1\\0&1&-8\\-3&4&1/3 \end{array}\right\left|\begin{array}{ccc}2&3\\0&1\\-3&4\end{array}\right|\\\\\\detA=2.1.\dfrac{1}{3}+3.(-8).(-3)+1.0.4-3.0.\dfrac{1}{3} -2.(-8).4-1.1.(-3)\\\\detA=\dfrac{2}{3} +72+0-0+64+3\\\\detA=\dfrac{2}{3}+139\\\\detA=\dfrac{2}{3}+\dfrac{417}{3}\\\\\boxed{\boxed{detA=\dfrac{419}{3}}}$