Answer to Question #60689 in Math for esita

Question

b) Find the eigenvalue of the matrix A, nearest to 2 and also the corresponding eigenvector
using four iterations of the inverse power method where











−
− −
−
=
0 1 4
1 4 1
4 1 0
A (6)
5. a) i) Set up the Gauss-Seidel iteration scheme in matrix form for solving the system of
equations
7 2x x 1 − 2 =
1 x 2x x − 1 + 2 − 3 =
1 x 2x − 2 − 3 =
ii) Show that this iteration scheme converges and find the rate of convergence.
iii) Perform two iterations of this method taking the zero vector as the initial
approximation. (6)
b) Find the inverse of the matrix











= − −
1 2 4
2 3 5
3 1 2
A
using LU decomposition method