Question

Solve the system of equation by guess jordan method

2x1-6x2-2x3=14, 3x1+4x2-7x3= 16, 3x1-6x2+9x3=21

Answer 1

Answer with explanation:

The System of equations which we have to solve by Gauss Jordan Method:

`1.\rightarrow 2x_(1)-6x_(2)-2x_(3)=14, 2.\rightarrow 3x_(1)+4x_(2)-7x_(3)= 16, 3.\rightarrow 3x_(1)-6x_(2)+9x_(3)=21`

Writing it in the form of Augmented Matrix=3 Rows and 4 Columns:

`\left[\begin{array}{cccc}2&-6&-2&14\\3&4&-7&16\\3&-6&9&21\end{array}\right]\\\\R_(1)=(R_(1))/(2),R_(3)=(R_(3))/(3)\\\\ \left[\begin{array}{cccc}1&-3&-1&7\\3&4&-7&16\\1&-2&3&7\end{array}\right]\\\\R_(3)\rightarrow R_(3)-R_(1)\\\\\left[\begin{array}{cccc}1&-3&-1&7\\3&4&-7&16\\0&1&4&0\end{array}\right]\\\\R_(2)\rightarrow R_(2)-3R_(1)\\\\\left[\begin{array}{cccc}1&-3&-1&7\\0&13&-4&-5\\0&1&4&0\end{array}\right]`

`R_(3)\rightarrow R_(2)+R_(3)\\\\\left[\begin{array}{cccc}1&-3&-1&7\\0&13&-4&-5\\0&14&0&-5\end{array}\right]\\\\\rightarrow14 x_(2)= -5\\\\x_(2)=(-5)/(14)\\\\\rightarrow 13 x_(2)-4x_(3)=-5\\\\ (-65)/(14)-4 x_(3)=-5\\\\-4x_(3)=-5+(65)/(14)\\\\x_(3)=(5)/(56)\\\\x_(1)-3x_(2)-x_(3)=7\\\\x_(1)+(15)/(14)-(5)/(56)=7\\\\x_(1)+(55)/(56)=7\\\\x_(1)=7-(55)/(56)\\\\x_(1)=(337)/(56)`

Solution set

`=((337)/(56),(-5)/(14),(5)/(56))`