Question

Calcule o determinante

Answer 1

Explicação passo-a-passo:

Usando a Regra de Sarrus:

$\left|\begin{array}{ccc}x&0&1\\1&x&1\\1&1&1\end{array}\right| =0\\\\\\\left|\begin{array}{ccc}x&0&1\\1&x&1\\1&1&1\end{array}\right\left|\begin{array}{ccc}x&0\\1&x\\1&1\end{array}\right|=0\\\\x.x.1+0.1.1+1.1.1-0.1.1-x.1.1-1.x.1=0\\\\x^{2} +0+1-0-x-x=0\\\\x^{2} -2x+1=0\\\\\Delta=(-2)^{2}-4.1.1=4-4=0\\\\x=\dfrac{-(-2)\pm\sqrt{0} }{2.1} \\\\x= \dfrac{2}{2}\\\\\boxed{\boxed{x=1} }$