Find the approximation of the jaobi's method and gauss-seidel method for the following linear system, using 𝑥(0) = 0 :
10𝑥1 - 𝑥2 = 9,
-𝑥1+10𝑥2 - 2𝑥3 = 7,
-2𝑥2 + 10𝑥3 = 6.
To begin, solve the 1st equation for , the 2nd equation for and so on to obtain the rewritten equations:
We can apply the Jacobi method of iteration as follows: