Question

Solve by Gauss Elimination method 2x+y+z=10 ,3x+2y+3z=18,x+4y+9z=16(Write Row operations and values of x ,y and z as answer )​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The values are x = 7, y = -9, z = 5.

Step-by-step explanation:

The given equations are

2x+y+z = 10

3x+2y+3z = 18

x+4y+9z = 16

The given equations in the matrix form are given by

$A = \left[\begin{array}{4444}2&1&1&\begin{tabular{|}}10\\3&2&3&18\\1&4&9&16\end{array}\right]$ $R_{1}/2$  → $R_{1}$

   $= \left[\begin{array}{4444}1&0.5&0.5&5\\3&2&3&18\\1&4&9&16\end{array}\right]$ $R_{2}-3R_{1}$ → $R_{2}$

   $= \left[\begin{array}{4444}1&0.5&0.5&5\\0&0.5&1.5&3\\0&3.5&8.5&11\end{array}\right]$  $R_{2} / 0.5$ → $R_{2}$

   $= \left[\begin{array}{4444}1&0.5&0.5&5\\0&1&3&6\\0&3.5&8.5&11\end{array}\right]$  $R_{1}-0.5R_{2}$ → $R_{1}$

   $= \left[\begin{array}{4444}1&0&-1&2\\0&1&3&6\\0&0&-2&-10\end{array}\right]$  $R_{3}/(-2)$ → $R_{3}$

   $= \left[\begin{array}{4444}1&0&-1&2\\0&1&3&6\\0&0&1&5\end{array}\right]$  

    $R_{1} +R_{3}$ → $R_{1}$

    $R_{2}-3R_{3}$ → $R_{2}$

  $= \left[\begin{array}{4444}1&0&0&7\\0&1&0&-9\\0&0&1&5\end{array}\right]$

Therefore the values are x = 7, y = -9, z = 5.