## 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

x = 2

y = 1

z = 3

 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 3) Find the following linear equations by using rank method of matrix 2x + 5y + 7z = 52x + y + z = 92x + y - z = 0 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 4 ranking method examples 4 Solution Rank Method Question4 to Examples 