Question

The question is as follows:

Assume that for some sytem of equations Aj = b

A:

2	1	-1
-1.5	3	0.75
0.25	0.5	1

b:

4

9

-3

If the Gauss Siedel method were used to solve the system of equations, what would C and d be? (Fill in the blanks)

C:

d:

Answer 1

Given, A = and b =

In Gauss-Seidel method, we reduce the given augmented matrix into row reduced echelon form.

Here, the augmented matrix is = (A|b)

=

Now, we apply elementary row operations on the augmented matrix.

Step I : R₂+(3/4)R₁=R₂, R₃-(1/8)R₁=R₃

Then we get,

Step II : (4/3)R₂=R₂

Then we get,

Step III : R₁-(1/5)R₂=R₁, R₃-(0.075)R₂=R₃

Then we get,

Step IV : R₁+(1/1.125)R₃=R₁

Then we get,

Step V : (1/2)R₁=R₁, (1/5)R₂=R₂, (1/1.125)R₃=R₃

Then we get,

Therefore, C = and d = .