Question

x+y+z=5;2x-y+z=9;x-2y+3z=26​

Answer 1

Answer:

(- 2/9, - 19/9, 22/3)

Step-by-step explanation:

x + y + z = 5

2x - y + z = 9

x - 2y + 3z = 26

$A=\left[\begin{array}{ccc}1&1&1\\2&-1&1\\1&-2&3\end{array}\right] = - 9$

$A_{x}=\left[\begin{array}{ccc}5&1&1\\9&-1&1\\26&-2&3\end{array}\right] =2$

$A_{y}= \left[\begin{array}{ccc}1&5&1\\2&9&1\\1&26&3\end{array}\right] =19$

$A_{z} =\left[\begin{array}{ccc}1&1&5\\2&-1&9\\1&-2&26\end{array}\right] =-66$

x = $\frac{A_{x} }{A}$ = $-\frac{2}{9}$

y = $\frac{A_{y}}{A}$ = $- \frac{19}{9}$

z = $\frac{A_{z} }{A}$ = $\frac{-66}{-9}=\frac{22}{3}$