Solve each item supporting your answer with clear explanation. 1.Consider the following augmented matrix of a...

Solve each item supporting your answer with clear explanation.

1.Consider the following augmented matrix of a system of linear equations.

( 7 −3 4 6

−3 2 6 2

2 5 3 −5 )

a. Solve the system with the Jacobi method. First rearrange to make it diagonally dominant if possible. Use [0,0,0] as the starting vector. Find the condition number of the matrix of coefficients κ_∞(A), and compute how many iterations are required to get the solution accurate to five significant digits?

b. Repeat part a) using the Gauss-Seidel method. Are fewer iterations required?

c. Is convergence faster in parts a) and b) if the starting vector is [-0.26602, -0.26602,-0.26602]?

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Expert Solution

Colby Messinger answered 1 year ago

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