Page 108 - MATLAB an introduction with applications

MATLAB Basics ——— 93

P1.44: Determine the eigenvalues and eigenvectors of the following matrices using MATLAB.
 1 − 2
(a) A =  
 1 3 
 1 5
(b) A =  
 − 24 
P1.45: Determine the eigenvalues and eigenvectors of A B using MATLAB.
*
3  − 1 2 1 1  2 5 7
 1 2 7 4   2 − 1 − 2 4 
A =  7  − 1 8 6  , B =  3  2 5 1 
   
1   − 2 3 4   4   1 − 3 6 
P1.46: Determine the eigenvalues and eigenvectors of A and B using MATLAB.
 4 5 − 3  1 2 3


A =− 12 3 , B =   8 9 6  


  2 5 7     5 3 − 1 
P1.47: Determine the eigenvalues and eigenvectors of A = a b using MATLAB.
*
6  − 3 4 1 
 0 4 2 6 
a =  1  3 8 5  
 
2   2 1 4  
0  1 2 3
 4 5 6 − 1 
 
b =  1 5 4 2
 
2   − 3 6 7 

P1.48: Determine the values of x, y and z for the following set of linear algebraic equations:
x – 3x =–7
2 3
2x + 3x – x =9
1 2 3
4x + 5x – 2x =15
1 2 3
P1.49: Determine the values of x, y and z for the following set of linear algebraic equations:
2x – y =10
–x + 2y – z =0
–y + z = –50
P1.50: Solve the following set of equations using MATLAB.
(a) 2x + x + x – x =12
3
4
2
1
x + 5x – 5x + 6x =35
1
4
3
2
– 7x + 3x – 7x – 5x =7
1
4
3
2
x – 5x + 2x + 7x =21
4
2
3
1
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