Question

Resolver o sistema abaixo pela Regra de Cramer.

8x + 4y +5z= -23
4x _ 8y +1z= -7
-2x - 10y +2z= 0

Answer 1

Primeiro passo é calcular o determinante da matriz $\left[\begin{array}{ccc}8&4&5\\4&-8&1\\-2&-10&2\end{array}\right]$ que dá -128.
Dx = $det\left[\begin{array}{ccc}-23&4&5\\-7&-8&1\\0&-10&2\end{array}\right]$ = 304
Dy = $det\left[\begin{array}{ccc}8&-23&5\\4&-7&1\\-2&0&2\end{array}\right]$ = 48
Dz = $det\left[\begin{array}{ccc}8&4&-23\\4&-8&-7\\-2&-10&0\end{array}\right]$=64
$x = \frac{Dx}{D}= \frac{304}{-128} = -2,375\\ y = \frac{Dy}{D}= \frac{48}{-128} =-0,375\\ z=\frac{Dz}{D}= \frac{64}{-128} =-0,5$