Hi,I need an answer for those questions , I have to show my work

Question

Robert · Accepted Answer

Q4. Given   (
   
    
   
) 
A.  
    ( )  |
   
    
   
| 
Using row transformation          
    ( )  |
     
    
   
| 
                       (   )(     ) 
The value of this determinant can be 0 for any given x if y is 4 and for any given y if x is -10.5. 
Hence there cannot be a unique value of x or y that makes the given matrix nonsingular. 
B.    ( )                                     
                 (
 (     )  (    ) (    )
  (   )   (   )
       (   )    
) 
   ( )  (
 (     )       
 (    )  (   )   (   )
(    )   (   )    
) 
    
 
    
   ( ) 
    
 
(     )(   )
(
 (     )       
 (    )  (   )   (   )
(    )   (   )    
) 
      
 
(     )(   )
(
 (     )       
 (    )  (   )   (   )
(    )   (   )    
)(
   
    
   
) 
                
 
(     )(   )
(
(   )(     )   
 (   )(     )  
  (   )(     )
) 
               (
   
   
   
)
Q5. Given                                          
i.
ii. The recurrence relation is given by, 
(
    
  
    
)  (
     
   
   
)(
  
    
    
) 
The coefficient matrix is given by, 
  (
     
   
   
) 
The eigenvalues of the obtained coefficient matrix are obtained using, 
|    |    
|
       
    
    
|    
   (   )
 (   )(   )(   )    
Hence the eigenvalues of the coefficient matrix are -2, 3 and 6. 
The eigenvectors corresponding to the given eigenvalues are, 
  (
    
    
   
) 
   ( )  (
      
      
     
) 
And 
    
 
   
(
      
      
     
) 
Hence the diagonalized form is given by,
Here   (
    
   
   
) is the diagonal matrix with the eigenvalues as its diagonal elements. 
  (
    
    
   
)(
    
   
   
)
(
 
 

   
 

 

   
 
   
 

   )
 
 

We know that, 
(
    
  
    
)  (
     
   
   
)
   
(
  
  
  
)
Using the diagonalisation method, we can say that,

Hi, I need an answer for those questions , I have to show my work

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