## 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

x = -1

y = 6

z = 4

 Questions Solution 1) Find the following linear equations by using rank method of matrix 2x + y + z = 5x + y + z = 4x - y + 2z = 1 Solution 2) Find the following linear equations by using rank method of matrix x + 2y + z = 72x - y + 2z = 4x + y - 2z = -1 Solution 4) Find the following linear equations by using rank method of matrix 3x + y - z = 22x - y + 2z = 62x + y - 2z = -2 Solution 5) Find the following linear equations by using rank method of matrix 2x - y + 3z = 9x + y + z = 6x - y + z = 2 ranking method examples 3 ranking method examples 3 Solution Rank Method Question3 to Examples 