Question

2.Test the consistency of following system of linear equations and hence find the solution 4x-y=12,-x+5y-2z=0,-2y+4z=-8​

Answer 1

Step-by-step explanation:

Here the number of unknowns = 3.

The matrix form of the system is AX = B where (i.e) AX = B

The augmented matrix (A, B) is Applying Gaussian elimination method on [A,B] we get

The above matrix is in echelon form also ρ(A, B) = ρ(A) = 3 = number of unknowns

The system of equations is consistent with a unique solution.

To find the solution. Now writing the equivalent equations we get x – y + 2z = 2 3y = 3 ⇒ y = 1 7z = -7 ⇒ z = 1 Substituting z = y = 1 in (1) we get x – 1 + 2 = 2 ⇒ x = 1 ⇒ x = y = z

Hope this will help you buddy...✌️

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