Ranking Method Examples 2





In this page ranking method examples 2 we are going to see solution of question 1 in rank method.

Question 2:

Solve the following linear equation by rank-method

x + 2y + z = 7

2x - y + 2z = 4

x + y - 2z = -1

Solution:

 
1 2 1 7
2 -1 2 4
1 1 -2 -1
 


˜
 
1 2 1 7
2 -1 2 4
1 1 -2 -1
 

R₂ => R₂ - 2R₁

         2         -1         2        4

         2          4         2        14

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

      _______________________

       0        -5         0       -10

      ________________________

R => R - R₁

        1          1        -2        -1

         1          2         1        -7

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

      ___________________________

       0        -1        -3       -8

      ____________________________

ranking method examples 2

˜
 
1 2 1 7
0 -5 0 -10
0 -1 -3 -8
 

R₃ => 5R - R

        0          -5        -15        -40

         0          -5         0          -10

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

      _______________________________

       0          0        -15       -30

      ______________________________

˜
 
1 2 1 7
0 -5 0 -10
0 0 -15 -30
 

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 + 2y + z = 7 --------(1)

-5y  = -10 --------(2)

   -15z = -30 --------(3)

       z = -30/(-15)

       z = 2

  - 5 y = -10

       y = -10/(-5)

        y = 2

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

 x + 2 (2) + 2 = 7

  x + 4 + 2 = 7

     x + 6 = 7

          x = 7 - 6

          x = 1

Answer :

 x = 1

 y = 2

 z = 2


Questions



Solution


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

2x + y + z = 5

x + y + z = 4

x - y + 2z = 1

ranking method examples 2 

Solution

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

2x + 5y + 7z = 52

x + y + z = 9

2x + y - z = 0

Solution

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

3x + y - z = 2

2x - y + 2z = 6

2x + y - 2z = -2

Solution

5) Find the following linear equations by using rank method of matrix

2x - y + 3z = 9

x + y + z = 6

x - y + z = 2

Solution







Rank Method Question2 to Examples
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