Question

solve the equation x-y+2z=4, 3x+y+4z=6,x+y+z=1 using gauss elimination method​

Answer 1

sorry I write answer wrong

Answer 2

Given :

x-y+2z=4,

3x+y+4z=6,

x+y+z=1

To Find : Solve using gauss elimination method​

Solution:

x-y+2z=4,        

3x+y+4z=6,    

x+y+z=1          

$\left[\begin{array}{ccc}1&-1&2\\3&1&4\\1&1&1\end{array}\right| \left \begin{array}{ccc}4\\6\\1\end{array} \right]$

 R₂ →   R₂  - 3R₁

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

R₃ →   R₃  - R₁

$\left[\begin{array}{ccc}1&-1&2\\0&4&-2\\0&2&-1\end{array}\right| \left \begin{array}{ccc}4\\-6\\-3\end{array} \right]$

R₂ →   R₂/2

$\left[\begin{array}{ccc}1&-1&2\\0&2&-1\\0&2&-1\end{array}\right| \left \begin{array}{ccc}4\\-3\\-3\end{array} \right]$

R₃ →   R₃  - R₂

$\left[\begin{array}{ccc}1&-1&2\\0&2&-1\\0&0&0\end{array}\right| \left \begin{array}{ccc}4\\-3\\0\end{array} \right]$

R₁ →   R₁ + 2R₂

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

Solution :

x + 3y = -2

2y - z  = -3

Infinite solutions:

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