Solving Linear Equations in Three Variables Using Rank Method :
Problem 1 :
Solve the following linear equations by rank method
2x + y + z = 5, x + y + z = 4, x - y + 2z = 1
Solution :
|
ranking method examples 1 |
|
|||||||||||||||||
R₂ <-> R₂ |
|
|||||||||||||||||
R₂ => R₂ - 2R₁ |
2 1 1 5 -2 -2 -2 -8 ---------------------------- 0 -1 -1 -3 | |||||||||||||||||
R₃ => R₃ - R₁ |
1 -1 2 1 1 1 1 4 --------------------------- 0 -2 1 -3 | |||||||||||||||||
ranking method examples 1 |
|
|||||||||||||||||
R₃ => R₃ - 2R₂ |
0 -2 1 -3 0 +2 +2 +6 ---------------------------- 0 0 3 3 |
|
R₃ => R₃ - 2R₂ |
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 = 4 --------(1)
-y - z = -3 --------(2)
3z = 3 --------(3)
z = 1
Apply z = 1 the second equation to get the value of y
- y - 1 = -3 and y = 2
Apply z = 1 and y = 2 in the first equation to get the value of x
x + 3 = 4
x = 1
Solution :
x = 1, y = 2 and z = 1
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Apr 23, 24 09:10 PM
Apr 23, 24 12:32 PM
Apr 23, 24 12:07 PM