Page 107 - MATLAB an introduction with applications

92 ——— MATLAB: An Introduction with Applications

Using MATLAB, determine the following:
(a) A + B
(b) AB
(c) A 2
(d) A T
(e) B –1
(f ) B A
T T
2
2
(g) A + B – AB
(h) det A, det B and det AB.
P1.40: Find the inverse of the following Matrices:
 3 2 1 

(a) A =− 15 4  

  5 7 − 9 
 1 6 3

(b) B =− 4 − 5 7  

  8 4 2 
 − 1 − 2 5 

(c) C =− 4 7 2  

  7 − 8 − 1 
P1.41: Determine the eigenvalues and eigenvectors of the following matrices using MATLAB.

 1 − 2  1 5
A =   , B =  
 1 5   − 2 7 

 4 6 2
P1.42: If A =   5 6 7  
  1058 

Use MATLAB to determine the following:
(a) the three eigenvalues of A
(b) the eigenvectors of A
(c) Show that AQ = Qd where Q is the matrix containing the eigenvectors as columns and d is the
matrix containing the corresponding eigenvalues on the main diagonal and zeros elsewhere.
P1.43: Determine eigenvalues and eigenvector of A using MATLAB.
 0.5 − 0.8
(a) A =  
 0.75 1.0 
 8 3
(b) A =  
 − 34 

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