Ranking Method Examples 4





In this page ranking method examples 4  we are going to see solution of question 4 in rank method.

Question 4:

Solve the following linear equation by rank-method

3x + y - z = 2

2x - y + 2z = 6

2x + y - 2z = -2

Solution:

 
3 1 -1 2
2 -1 2 6
2 1 -2 -2
 


˜
 
3 1 -1 2
2 -1 2 6
2 1 -2 -2
 

C₁ <-> C₂

˜
 
1 3 -1 2
-1 2 2 6
1 2 -2 -2
 

R₂ => R₂ + R₁

        -1       2          2        6

         1         3         -1        2

      _______________________

       0        5          1        8

      _______________________

R => R - R₁

       1         2          -2       -2

         1         3         -1        2

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

      ________________________

       0        -1        -1        -4

      _________________________

˜
 
1 3 -1 2
0 5 1 8
0 -1 -1 -4
 

R => 5 R + R

         0         -5          -5       -20

         0          5           1          8

      _________________________

       0          0          -4       -12

      _________________________

ranking method examples 4 ranking method examples 4

˜
 
1 3 -1 2
0 5 1 8
0 0 -4 -12
 

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 + 3y - z = 2   --------(1)

5y + z = 8  --------(2)

-4z = -12 --------(3)

   z = -12/(-4)

   z = 3

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

 5y + 3 = 8

      5y = 8 - 3

      5y = 5

       y = 1

substitute z = 3 and y = 1 in the first equation to get the value of x

  x + 3(1) - 3 = 2

   x + 3 - 3 = 2

   x = 2

Answer :

 x = 2

 y = 1

 z = 3


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

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

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 4 ranking method examples 4

Solution







Rank Method Question4 to Examples
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