SKEDSOFT

Problems on Solving Linear System:

Example-1 Solve the system of linear equations: x y z = 1, 3x y − 3z = 5, x − 2y − 5z = 10 by Crout’s method.

Solution: Here,

Let the auxillary matrix

where,

Thus, the solution is

Example-2 Apply Gauss-Seidal iteration method to solve the equation 20x y − 2z = 17, 3x 20y − z = −18, 2x − 3y 20z = 25

Solution: Write the given equation in the form;

First Iteration,

Putting y = y₀, z = z₀ in Equation, we get

Putting x = x₁, z = z₀ in equation above, we have