Question

Solve by Gauss - Jordan Elimination
method
x + y + z = 3
2x + 3y +7z = 0
x + 3y - 2z = 17​

Answer 1

Given :

x + y + z = 3

2x + 3y + 7z = 0

x + 3y - 2z = 17

To find :

Value of x , y , z.

​Solution :

x + y + z = 3

2x + 3y + 7z = 0

x + 3y - 2z = 17

$\left[\begin{array}{ccc}1&1&1|3\\2&3&7|0\\1&3&-2|17\end{array}\right]$

R₂ → R₂ - 2R₁

R₃ → R₃ - R₁

$\left[\begin{array}{ccc}1&1&1|3\\0&1&5|-6\\0&2&-3|14\end{array}\right]$

R₁ → R₁ - R₂

R₃ → R₃ - 2R₂

$\left[\begin{array}{ccc}1&0&-4|9\\0&1&5|-6\\0&0&-13|26\end{array}\right]$

R₃ → -1/13R₃

$\left[\begin{array}{ccc}1&0&-4|9\\0&1&5|-6\\0&0&1|-2\end{array}\right]$

R₁ → R₁ + 4R₃

R₂ → R₂ - 5R₃

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

So, from above matrix

x = 1

y = 4

z = -2