## 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

x = 1

y = 2

z = 3

 Questions Solution 1) Solve the following linear equations by using rank method of matrix 2x + y + z = 5x + y + z = 4x - y + 2z = 1 Solution 2) Solve the following linear equations by using rank method of matrix x + 2y + z = 72x - y + 2z = 4x + y - 2z = -1 Solution 3) Solve the following linear equations by using rank method of matrix 2x + 5y + 7z = 52x + y + z = 92x + y - z = 0 Solution 4) Solve the following linear equations by using rank method of matrix 3x + y - z = 22x - y + 2z = 62x + y - 2z = -2 ranking method examples 5 ranking method examples 5 Solution Rank Method Question5 to Examples 