Question

Calcule o determinante para as matrizes de Vandemonde.
(ME AJUDEM)

Answer 1

Resposta:

$\frac{-1}{288}$

Explicação passo a passo:

$\left|\begin{array}{ccc}1&1&1\\1/2&1/3&1/4\\1/4&1/9&1/16\end{array}\right|=1\cdot\left|\begin{array}{ccc}1/3&1/4\\1/9&1/16\\\end{array}\right|-1\cdot\left|\begin{array}{ccc}1/2&1/4\\1/4&1/16\\\end{array}\right|+1\cdot\left|\begin{array}{ccc}1/2&1/3\\1/4&1/9\\\end{array}\right|=\frac{-1}{144} +\frac{1}{32} -\frac{1}{36} =-\frac{1}{288}$