Question

determine a solução da equação
2 x x |
-1 -2 -1 | = 2
3 -1 2 |

Answer 1

Equação:

$\displaystyle \left|\begin{array}{ccc} 2 & x & x \\ -1 & -2 & -1 \\ 3 & -1 & 2 \end{array}\right| = 2$

Para encontrar-mos o determinante dessa matriz, aplicamos a regra de Sarrus:

$\displaystyle \left|\begin{array}{ccc} 2 & x & x \\ -1 & -2 & -1 \\ 3 & -1 & 2 \end{array}\right| \left.\begin{array}{cc} 2 & x \\ -1 & -2 \\ 3 & -1 \end{array}\right. = 2$

$\displaystyle +2 \cdot (-2) \cdot 2 + x \cdot (-1) \cdot 3 \\ + x \cdot (-1) \cdot (- 1) \\ - 3 \cdot (-2) \cdot x - (-1) \cdot (-1) \cdot 2 \\ - 2 \cdot (-1) \cdot x = 2$

$\displaystyle -8 -3x + x + 6x -2 + 2x = 2$

$\displaystyle -3x +x + 6x +2x = 2 + 8 +2$

$\displaystyle -2x +8x =12$

$\displaystyle 6x = 12$

$\displaystyle x = \frac{ 12}{6 }$

$\displaystyle x = 2$

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