Question

Решить систему уравнений матричным методом

Answer 1

$\Delta =\left|\begin{array}{ccc}3&-3&1\\9&0&2\\5&-2&-1\end{array}\right|=3\cdot 4-3\cdot 19-18=-63\\\\\\\Delta _{x}=\left|\begin{array}{ccc}2&-3&1\\16&0&2\\9&-2&-1\end{array}\right|=2\cdot 4-3\cdot 34-32=-126$

$\Delta _{y}=\left|\begin{array}{ccc}3&2&1\\9&16&2\\5&9&-1\end{array}\right|=-3\cdot 34+2\cdot 19+1=-63\\\\\\\Delta _{z}=\left|\begin{array}{ccc}3&-3&2\\9&0&16\\5&-2&9\end{array}\right|=3\cdot 32+3\cdot 1-2\cdot 18=63\\\\\\x=\dfrac{\Delta _{x}}{\Delta }=\dfrac{-126}{-63}=2\ \ ,\ \ y=\dfrac{\Delta _{y}}{\Delta }=\dfrac{-63}{-63}=1\ \ ,\ \ z=\dfrac{\Delta _{z}}{\Delta }=\dfrac{63}{-63}=-1$

$Otvet:\ \ x=2\ ,\ y=1\ ,\ z=-1\ .$