Solving Linear Equations in Three Variables Using Rank Method :
Question 1 :
Test for consistency and if possible, solve the following systems of equations by rank method.
(iii) 2x + 2y + z = 5, x − y + z =1, 3x + y + 2z = 4
Solution :
ρ (A) = 3, ρ ([A| B]) = 2
Since the ranks of matrices A and [A, B} are not equal, it has no solution.
(iv) 2x − y + z = 2, 6x − 3y + 3z = 6, 4x − 2y + 2z = 4
Solution :
ρ (A) = 1, ρ ([A| B]) = 1
Since the ranks of matrices A and [A, B] are equal and it is less than 3, it has infinitely many solution.
2x - y + z = 2
Let y = s and z = t
2x - s + t = 2
2x = 2 + s - t
x = (2 + s - t)/2
Hence the solution is ((2 + s - t)/2, s, t) where s,t belongs to R.
After having gone through the stuff given above, we hope that the students would have understood, "Solving Linear Equations in Three Variables Using Rank Method".
Apart from the stuff given in this section, 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
Dec 02, 22 04:18 PM
Dec 02, 22 07:27 AM
Dec 02, 22 07:16 AM