Question

5x - 6y + 4z=15
7x + 4y - 3z=19
2x + y + 6z=46
Find the solutions of x , y and z using Gauss- Jordan method.​

Answer 1

Answer:

This is my answer

Step-by-step explanation:

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Answer 2

Given :

5x - 6y + 4z=15

7x + 4y - 3z=19

2x + y + 6z=46

x=?,y=?,z=?

Step-by-step explanation:

The above equations can be written in matrix form as  

⎡5 −6 4⎤   ⎡x⎤    ⎡15 ⎤

⎢7  4 -3⎥   ⎢y⎥ = ⎢19 ⎥ or AX = B

⎣2  1   6⎦   ⎣z⎦    ⎣46⎦  

               |5  -6  4|

|A| = D =  |7  4   -3|  

                |2  1    6|  

Apply   $C_{1}$  −2$C_{2}$ ,$C_{3}$ −6$C_{2}$ to make two zeros in $R_{3}$

​       |17  -16 40|    

D= |-1    4  -27|

     |0    1     0 |  

  = - |17   40|

       |-1   -27|

  =−[−459+40]=419 ≠0.  

∴ The matrix A is non-singular or rank of matrix A is  3. We will have a unique solution and the equations are consistent.  

By Crammer's rule  

x/$D_{1}$=y/$D_{2}$=z/$D_{3}$=1/D

Where $D_{1}$ is obtained from D by replacing the first column of D by b's i.e.15,19,46  

      |15  -6  4|

$D_{1}$= |19  4  -3|

      |46  1   6|

  =15(27)−19(−40)+46(2)=1257  

∴  x/1257  =  y/1676  =  z/2514  = 1/419  

∴x=3,y=4,z=6.

The solutions of x=3 , y =4and z =6