Question

Solve the system of equation by guess jordan method

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:

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

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

Solution set

  $=(\frac{337}{56},\frac{-5}{14},\frac{5}{56})$