Question

2x+4y+z=5
x +y +z=6
2x+3y+z =6

Solve this equation using row reduction method /gauss method

Answer 1

Step-by-step explanation:

step by step answer pls. all answer give pls

Answer 2

Answer:

The values are x = 2, y = -1, z = 5.

Step-by-step explanation:

The given equations are

2x+4y+z = 5

x+y+z = 6

2x+y+z = 6

The given equations in the matrix form are given, by

$A = \left[\begin{array}{4444}2&4&1&5\\1&1&1&6\\2&3&1&6\end{array}\right]$  $R_{1}/2$ → $R_{1}$

   $= \left[\begin{array}{4444}1&2&0.5&2.5\\1&1&1&6\\2&3&1&6\end{array}\right]$  

      $R_{2} -1$ → $R_{2}$

      $R_{3} - 2 R_{1}$ → $R_{3}$

$= \left[\begin{array}{4444}1&2&0.5&2.5\\0&-1&0.5&3.5\\0&-1&0&1\end{array}\right]$  $R_{2}/(-1)$  → $R_{2}$

$= \left[\begin{array}{4444}1&2&0.5&2.5\\0&1&-0.5&-3.5\\0&-1&0&1\end{array}\right]$

   $R_{1}-2R_{2}$ → $R_{1}$

   $R_{3}+ R_{2}$ → $R_{3}$

$= \left[\begin{array}{4444}1&0&1.5&9.5\\0&1&-0.5&-3.5\\0&0&-0.5&-2.5\end{array}\right]$  $R_{3} / (-0.5)$ → $R_{3}$

   $R_{1} - 1.5R_{3}$ → $R_{1}$

  $R_{2}+ 0.5R_{3}$ → $R_{2}$

$= \left[\begin{array}{4444}1&0&0&2\\0&1&0&-1\\0&0&1&5\end{array}\right]$

Therefore the values are x = 2, y = -1, z = 5.