Question

Marque a alternativa correta abaixo:
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Answer 1

É só fazer o determinante da matriz de terceira ordem, pela regra de Sarrus:

$[1 \cdot (-1) \cdot 0 + 2 \cdot 5 \cdot \frac{2}{3} + 3 \cdot (-\frac{1}{2})\cdot x] - [3 \cdot (-1) \cdot \frac{2}{3} + 5 \cdot (-\frac{1}{2}) \cdot 1 + 2 \cdot 0 \cdot x] = 0$

$0 + \frac{20}{3} - \frac{3}{2}x - [-2 - \frac{5}{2}] = 0\\\\\frac{20}{3} - \frac{3}{2}x + 2 + \frac{5}{2} = 0\\\\\\-\frac{3}{2}x = -2 - \frac{5}{2} - \frac{20}{3}\\\\\frac{3}{2}x = 2 + \frac{5}{2} + \frac{20}{3}\\\\\frac{3}{2}x = \frac{12 + 15 + 40}{6}\\\\\frac{3}{2}x = \frac{67}{6}\\\\x = \frac{67}{6}\times \frac{2}{3}\\\\x = \frac{67}{9}$

Ou seja, a alternativa correta é a letra E.