NUMERICAL ANALYSIS HOMEWORK 3 2015 (WEEK 3-4)

PROBLEM 1

Solve system of equation by using
a) By using Gauss elimination
b) By using Gauss-Jordan elimination
by hand

PROBLEM 2

Solve system of equation by using

a) By using Gauss elimination

b) By using Gauss-Jordan elimination

by hand and by computer program

Exact solution:

PROBLEM 3

Solve system of equation by using (computer programs)

a) By using Gauss elimination

b) By using Gauss-Jordan elimination

c) LU decomposition (Dolittle)

d) LU Craut Decomposition

PROBLEM 4

Solve system of equation by using

a) By using Gauss elimination

b) Gauss-Seidel iteration

c) Conjugate gradient method

PROBLEM 5

Solve system of equation by using Thomas algorithm (3 band matrix method)

PROBLEM 6

Load Matrix of the figure can be given with the following system of equations by any computer program you want

Where c=cos(q),s=sin(q) . For q =60^o find the load distribution profile

PROBLEM 7

For the given electrical circuit current density-Voltage eqautions can be given as:

Calculate current densities for R=10 W.

PROBLEM 8

-x₁ + 3x₂ + 5x₃ + x₄ = 8

x₁ +9x₂ + 3x₃ + 4x₄ = 10

x₂ +x₄ = 2

3x₁ + x₂ +x₃ - x₄ = -4

Solve the given system of equations. Determine the best method to solve it.

PROBLEM 9 Find infinite norm two norm and m=3 norm of the matrix by hand and by computer program

PROBLEM 10

Find the inverse matrix

PROBLEM 11

Find two norm, infinite norm and and inverse matrix