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consider the following system of linear equations 2 quad 2 x_1 6 x_2 x

Question

Advanced Mathematics

Consider the following system of linear equations:

2 \quad 2 x_{1}-6 x_{2}-x_{3}=-15

3-3 x_{1}-x_{2}+7 x_{3}=-35

-8 x_{1}+x_{2}-2 x_{3}=21

a) Solve the system of equations using matrix operations in Matlab (inv and/or backslash \).

b) Starting with initial guesses: x1 = x2, = x3, = 0, show two complete iterations using Gauss-Seidel iterative method. Evaluate the true and approximate errors of the second iteration.

c) Redo part (2) using Jacobi Iterative methods.

d) Redo part (2) using Gauss-Seidel with relaxation, with 2=0.8.

e) Solve the system of linear equations by calling GaussSeidel dsolve or Isolvep, whicheverapplicable for the methods below. Report the number of iterations needed for achieving 6significant figures accuracy.

i. Gauss-Seidel iterative method.

11.Jacobi iterative method. Print the iterations in a table format.

iii. Gauss-Seidel with relaxation, with 1 = 0.8 and 2 = 1.25.

iv. Compare the convergences in parts (a) to (c).

Answer

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Question 44046

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\text { The minimum change is }-15 e^{-28} \sqrt{445} ; \text { in the direction }\left(315 e^{-28},-30 e^{-28}\right)
\text { The maximum change is } 15 e^{28} \sqrt{445} ; \text { in the direction }\left(315 e^{28},-30 e^{28}\right\rangle
\text { The minimum change is }-15 e^{28} \sqrt{445} ; \text { in the direction }\left\{-315 e^{28}, 30 e^{28}\right)
\text { The maximum change is } 15 e^{-28} \sqrt{445} ; \text { in the direction }\left(315 e^{-28},-30 e^{-28}\right)
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