## 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

x = 1

y = 2

z = 2

 Questions Solution 1) Find the following linear equations by using rank method of matrix 2x + y + z = 5x + y + z = 4x - y + 2z = 1 ranking method examples 2 Solution 3) Find the following linear equations by using rank method of matrix 2x + 5y + 7z = 52x + y + z = 92x + y - z = 0 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 Solution Rank Method Question2 to Examples 