Final Exam-Numerical Analysis for Scientists

1-Solve the system using Gaussian elimination method with partial pivoting.

2-Find all the eigenvalues of A and find the eigenvector corresponding
to the dominant eigenvalue.
(b) (3 marks) Perform one iteration of the power method starting with X0.
(c) (1 mark) What can you say about the convergence of the power method for the
matrix A? Justify your answer.