English, asked by balasri1803, 4 months ago

solve 2x + y + 6z = 9; 8x + 3y + 2z = 13; x + 5y + z = 17 by using gauss Seidel iteration method​

Answers

Answered by neetutiwari2222
4

Answer:

Given : q=0.05C V

A

=200V V

B

=100V

As the electric field is an conservative field, thus the work done in moving a charge from one point to another is path independent.

∴ W

BA

=q(V

A

−V

B

)=0.05(200−100)=5 J

Answered by hukam0685
0

Explanation:

Given:

2x+y+6z=9\\8x+3y+2z=13\\x+5y+z=17\\

To find: Solution of system of equations using Gauss Seidel iteration method

Solution:

In this method;First write the given equations in terms of x,y and z respectively.Then approximate the values of x,y and z by iteration.

The whole process is shown below:

2x+y+6z=9\\x=\frac{1}{2}(9-y-6z)...eq1\\\\8x+3y+2z=13\\y=\frac{1}{3}(13-8x-2z)..eq2\\\\x+5y+z=17\\z=17-x-5y... eq3\\\\

Now,Start the process of approximation

Put

x_0=y_0=z_0=0\\

put

y=y_0\\z=z_0\\

in first equation

x_1=\frac{1}{2}(9-y_0-6z_0)\\\\x_1=\frac{1}{2}(9)\\\\\bold{x_1=4.500}\\

y_1=\frac{1}{3}(13-8x_1-2z_0)\\\\y_1=\frac{1}{3}(13-8(4.500)-2(0))\\\\\bold{y_1=-7.6666}\\

z_1=17-x_1-5y_1\\\\\bold{z_1=50.8333}\\

For second iteration we have the values of x1,y1,z1

apply second iteration

x_2=\frac{1}{2}(9-y_1-6z_1)\\\\\bold{x_2=-144.1666}\\\\

y_2=\frac{1}{3}(13-8x_2-2z_1)\\\\\bold{y_2=354.8887}\\

z_2=17-x_2-5y_2\\\\\bold{z_2=-1613.2769}\\

For third iteration

x_3=\frac{1}{2}(9-y_2-6z_2)\\\\\bold{x_3=4666.8863}\\\\

y_3=\frac{1}{3}(13-8x_3-2z_2)\\\\\bold{y_3=-11365.1788}\\

z_3=17-x_3-5y_3\\\\\bold{z_3=52176. 0077}\\

On observing the values of x,y and z in each iteration,one can analyze that the values are very different(Deviation is very large)

Thus,

These linear equations can not be solve by Gauss Seidel iteration method.

Remark*: These equation can be solve by Gauss elimination Method.

Hope it helps you.

To learn more on brainly:

What is the limitation of Gauss-Seidel method?

a) It cannot be used for the matrices with non-zero diagonal elem

b) ...

https://brainly.in/question/18067036?utm_source=android&utm_medium=share&utm_campaign=question

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