Ranking Method Examples 3





In this page ranking method examples 3 we are going to see solution of question 3 in rank method.

Question 3:

Solve the following linear equation by rank-method

2x + 5y + 7z = 52

x + y + z = 9

2x + y - z = 0

Solution:

 
2 5 7 52
1 1 1 9
2 1 -1 0
 


˜
 
2 5 7 52
1 1 1 9
2 1 -1 0
 

R₁ <-> R₂

˜
 
1 1 1 9
2 5 7 52
2 1 -1 0
 

R₂ => R₂ - 2R₁

       2          5         7        52

         2          2         2        18

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

      ___________________________

       0        3          4        34

      __________________________

R => R - 2R₁

         2          1         -1        0

         2          2         2        18

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

      ___________________________

       0        -1        -3       -18

      ___________________________

˜
 
1 1 1 9
0 3 4 34
0 -1 -3 -18
 

R => 3R+ R₂

       0          -3         -9        -54

         0           3          4         34

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

      _____________________________

       0          0        -5        -20

      _____________________________

ranking method examples 3 ranking method examples 3

˜
 
1 1 1 9
0 3 4 34
0 0 -5 -20
 

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 = 9   --------(1)

3y + 4z = 34  --------(2)

       -5z = -20 --------(3)

          z = -20/(-5)

          z = 4

substitute z = 4 in the second equation to get the value of y

  3y + 4(4) = 34

  3y + 16 = 34

         3y = 34 - 16

         3y = 18

          y = 18/3

          y = 6

substitute z = 4 and y = 6 in the first equation to get the value of x

 x + 6 + 4 = 9

   x + 10 = 9

         x = 9 -10

         x = -1

Answer :

 x = -1

 y = 6

 z = 4        


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

Solution

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

x + 2y + z = 7

2x - y + 2z = 4

x + y - 2z = -1

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

ranking method examples 3 ranking method examples 3

Solution







Rank Method Question3 to Examples
HTML Comment Box is loading comments...