Question

Calcule o valor de x, a fim  de que o determinante da matriz A seja nulo (igual a zero)​

Answer 1

$\left[\begin{array}{ccc}1&2&1\\4&9&4\\1&x&x-3\end{array}\right] \left[\begin{array}{ccc}1&2\\4&9\\1&x\end{array}\right] \\\\\\9 \cdot (x-3)+2 \cdot 4 + 4 \cdot x - [2 \cdot 4 \cdot (x-3) + 4 \cdot x + 9] = 0\\9x - 27 + 8 + 4x - [8(x-3)+4x+9] = 0\\9x - 19 + 4x - [8x-24+4x+9] = 0\\13x - 19 - [12x - 15] = 0\\13x - 19 - 12x + 15 = 0\\13x - 12x = 19 - 15\\\boxed{x = 4}$