Question

Faça o escalonamento de:

$x + 2y -4z=1$
$2x+5y-7z=-2$
$3x+7y-9z=3$

Answer 1

$\begin{Bmatrix}x+2y-4z&=&1\\2x+5y-7z&=&-2\\3x+7y-9z&=&3\end{matrix}$

multiplica a primeira linha por -2 e some a segunda linha

$\begin{Bmatrix}x+2y-4z&=&1\\-2x-4y+8z+2x+5y-7z&=&-2-2\\3x+7y-9z&=&3\end{matrix}$

$\begin{Bmatrix}x+2y-4z&=&1\\y+z&=&-4\\3x+7y-9z&=&3\end{matrix}$

multiplique a primeira linha por -3 e some a terceira

$\begin{Bmatrix}x+2y-4z&=&1\\y+z&=&-4\\-3x-6y+12z+3x+7y-9z&=&3-3\end{matrix}$

$\begin{Bmatrix}x+2y-4z&=&1\\y+z&=&-4\\y-3z&=&0\end{matrix}$

Agora multiplique a segunda linha por -1 e some a terceira

$\begin{Bmatrix}x+2y-4z&=&1\\y+z&=&-4\\-y-z+y-3z&=&0+4\end{matrix}$

$\begin{Bmatrix}x+2y-4z&=&1\\y+z&=&-4\\4z&=&4\end{matrix}$

agora acabou, você tem seu sistema escalonado

$\begin{Bmatrix}x+2y-4z&=&1\\y+z&=&-4\\z&=&1\end{matrix}$

$\begin{Bmatrix}x+2y-4z&=&1\\y+1&=&-4\\z&=&1\end{matrix}$

$\begin{Bmatrix}x+2y-4z&=&1\\y&=&-5\\z&=&1\end{matrix}$

$\begin{Bmatrix}x+2*(-5)-4*1&=&1\\y&=&-5\\z&=&1\end{matrix}$

$\begin{Bmatrix}x-10-4&=&1\\y&=&-5\\z&=&1\end{matrix}$

$\boxed{\boxed{\begin{Bmatrix}x&=&15\\y&=&-5\\z&=&1\end{matrix}}}$

Espero que tenha entendido ;)