Question

X+y+z=4 x-y+z=10 x+y-z=6

Answer 1

Por escalonamento podemos utilizar os valores na matriz:

$\left[\begin{array}{ccc}1&1&1\\1&-1&1\\1&1&-1\end{array}\right]$ = $\left[\begin{array}{c}4\\10\\6\end{array}\right]$

Se fizermos L2-L1 e L3-L1:

$\left[\begin{array}{ccc}1&1&1\\0&-2&0\\0&0&-2\end{array}\right]$ = $\left[\begin{array}{c}4\\6\\2\end{array}\right]$

Depois, L1+$\frac{1}{2}$L3:

$\left[\begin{array}{ccc}1&1&0\\0&-2&0\\0&0&-2\end{array}\right]$ = $\left[\begin{array}{c}5\\6\\2\end{array}\right]$

Depois, L1+$\frac{1}{2}$L2:

$\left[\begin{array}{ccc}1&0&0\\0&-2&0\\0&0&-2\end{array}\right]$ = $\left[\begin{array}{c}8\\6\\2\end{array}\right]$

Portanto temos que:

x=8;

-2y=6;

-2z=2;

Ou seja:

x=8, y=-3 e z=-1.