Question

Solve the system of equations 8x + y + z = 8, 2x + 4y +z = 4, x + 3y + 3z = 5 by Gauss
Seidel methods.​

Answer 1

Answer:

What is this question

This is wrong

Answer 2

The value x is 1, Y is 1 and Z is 2

Given:

8x + y + z = 8, 2x + 4y +z = 4, x + 3y + 3z = 5

To Find:

The value of x, y and z using Gauss Seidel method

Solution:

The given equation can be written in matrix form,

$\left[\begin{array}{ccc}8&4&3\\2&1&1\\1&2&1\end{array}\right]$$\left[\begin{array}{ccc}x&\\y&\\z&\end{array}\right]$ = $\left[\begin{array}{ccc}18&\\5&\\5&\end{array}\right]$

AX = B

|A| = -3

Therefore, the above system has a unique solution,

X = $A^{-1}$B

Co-factors of A are,

C11 =  -1

upto c33 = 0

Adj A = $\left[\begin{array}{ccc}-1&-1&3\\2&5&12\\1&-2&0\end{array}\right]^T$

= $\left[\begin{array}{ccc}-1&2&1\\-1&5&-2\\3&-12&0\end{array}\right]$

X = $A^{-1}$ B

= $\frac{-1}{3}$$\left[\begin{array}{ccc}-1&-1&3\\2&5&12\\1&-2&0\end{array}\right]$$\left[\begin{array}{ccc}18&\\5&\\5&\end{array}\right]$

X = $\left[\begin{array}{ccc}18&\\1&\\2&\end{array}\right]$

So, X = 1, Y = 1 and Z = 2

#SPJ2