Ranking Method Examples 5





In this page ranking method examples 5 we are going to see solution of question 5 in rank method.

Question 5:

Solve the following linear equation by rank-method

2x - y + 3z = 9

x + y + z = 6

x - y + z = 2

Solution:

 
2 -1 3 9
1 1 1 6
1 -1 1 2
 


˜
 
2 -1 3 9
1 1 1 6
1 -1 1 2
 

R₁ <-> R₂

˜
 
1 1 1 6
2 -1 3 9
1 -1 1 2
 

R₂ => R₂ - 2R₁

          2          -1         3        9

         2          2          2        12

        (-)       (-)         (-)       (-)

      __________________________

       0       -3          1        -3

      _________________________

R => R - R₁

         1         -1         1        2

         1          1          1        6

        (-)       (-)         (-)      (-)

      ________________________

       0       -2          0        -4

      _________________________

ranking method examples 5 ranking method examples 5

˜
 
1 1 1 6
0 -3 1 -3
0 -2 0 -4
 

R₂ => R₂ - 2R₁

R => R - R₁

R => 3R- 2R₂

        0         -6          0       -12

         0         -6          2        -6

        (-)       (+)         (-)      (+)

      ________________________

       0         0          -2        -6

      _______________________

˜
 
1 1 1 6
0 -3 1 -3
0 0 -2 -6
 

Rank (A) = 3

Rank [A,B] = 3

If rank (A) = rank of [A,B] = number of unknowns then we can say that the system is consistent and it has unique solution.

x + y + z = 6   --------(1)

-3y + z = -3  --------(2)

       -2z = -6 --------(3)

         z = -6/(-2)

         z = 3

substitute z = 3 in the second equation to get the value of y

   -3y + 3 = -3

          -3y = -3 - 3

          -3y = -6

             y = -6/(-3)

             y = 2

substitute z = 3 and y = 2 in the first equation to get the value of x

     x + 2 + 3 = 6

      x + 5 = 6

            x = 6 - 5

            x = 1

Answer :

 x = 1

 y = 2

 z = 3


Questions



Solution


1) Solve the following linear equations by using rank method of matrix

2x + y + z = 5

x + y + z = 4

x - y + 2z = 1

Solution

2) Solve the following linear equations by using rank method of matrix

x + 2y + z = 7

2x - y + 2z = 4

x + y - 2z = -1

Solution

3) Solve the following linear equations by using rank method of matrix

2x + 5y + 7z = 52

x + y + z = 9

2x + y - z = 0

Solution

4) Solve the following linear equations by using rank method of matrix

3x + y - z = 2

2x - y + 2z = 6

2x + y - 2z = -2

ranking method examples 5 ranking method examples 5

Solution







Rank Method Question5 to Examples
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