Page 274 - MATLAB an introduction with applications

Numerical Methods ——— 259

PROBLEMS

P4.1: Use the method of Gaussian elimination to solve the following system of linear equations:
x + x + x – x = 2
4
2
1
3
4x + 4x + x – x = 11
1
2
3
4
x – x – x + 2x = 0
3
1
2
4
2x + x + 2x – 2x = 2
1
4
2
3
P4.2: Use Gaussian elimination method to solve the system of equations [A]{x} = {b} where
 1 1 1 1 3 
 2 − 1 3 0  
3

A =   , b = 
 0 2 0 3 
1
  
0
−   1 0 2 1  
P4.3: Solve the following set of equations by Gauss-Jordan method.
2x + x – 3x = 11
1
3
2
4x – 2x + 3x = 8
3
2
1
–2x + 2x – x = –6
3
1
2
P4.4: Use Gauss-Jordan method to solve the following set of equations.
 5 − 4 1 0 0  1  
x
 − 4 6 − 4 1 0   
1
2
   
x
 

 1 − 4 6 − 4 1   =  3 
2
x
    
3
2
 0 1 − 4 6 − 4    
x
  0 0 1 − 4 5     1  
4
P4.5: Solve the following system of equations using Choleski’s factorizations.
x + x + x – x = 2
1
4
2
3
x – x – x + 2x = 0
3
4
2
1
4x + 4x + x + x = 11
3
1
4
2
2x + x + 2x – 2x = 2
4
3
2
1
P4.6: Use Choleski’s method of solution for Problem P4.2.
P4.7: Use Jacobi iterative scheme to obtain the solutions of the following system of equations.
x + 2y + z = 0
3x + y – z = 0
x – y + 4z = 3
P4.8: Use Jacobi iterative scheme to obtain the solution for Problem P4.1.
P4.9: Use Gauss-Seidel method to solve the following system of equations in Problem P4.7.