- note: i needexpert(Norman Wagner) to do this assignment please.-see attachment thanks

Sol: 1 (a)
 
 
 
1 3
3 8 3
0 1 1
1 0
3 3
9 8
0 1
3 0
9
17
1
3
T a
T a
T a
 
 
        
 
 
 
 

 
 
 
 
 
 
 
 
 
 
(b) Augmented matrix  ,C A B
2 1 2 4 1 4
3 2 3 4 2 4
1 3 2
3 8 5
0 1 1
1 0 1
1 3 2
0 1 1
3 , ,
0 1 1
0 3 3
1 3 2
0 1 1
, 3 ,
0 0 0
0 0 0
C
R R R R R R
R R R R R R
  
 
 
 
 
 
 
  
 
       
 
 
 
  
 
       
 
 
 
So the rank of C is 2 and rank of A is 2.
    2R C R A 
Hence, the equations are consistent with unique solution.

1
2
1 3 2
0 1 1
0 0 0
0 0 0
x
x
    
   
         
   
   


1 2
2
3 2 ................... (1),
1 ..................(2),
x x
x
  


Put the value of
2x in equation (1), we get

1 1x 
So the solution is 1 21, 1 x x 
(c) Augmented matrix  ,C A B
2 1 2 4 1 4
1 3 1
3 8 1
0 1 1
1 0 1
1 3 1
0 1 2
3 , ,
0 1 1
0 3 0
C
R R R R R R
 
 

 
 
 
 
 
 

       
 
 
 
3 2 3 4 2 4
3 3
4 3 4
1 3 1
0 1 2
, 3 ,
0 0 3
0 0 6
1 3 1
0 1 2 1
,
0 0 1 3
0 0 6
1 3 1
0 1 2
6 ,
0 0 1
0 0 0
R R R R R R
R R
R R R
 
 

       
 
 
 
 
 

  
 
 
 
 
 

   
 
 
 
So the rank of C is 3 and rank of A is 2.
   R C R A
Hence, the equations are inconsistent.
Sol: (2) Linear transformation
4 2:T R R is defined by
   1 2 3 4 2 1 4 3, , , ,T x x x x x x x x  
(a) Standard matrix

1 0 0 0
0 0 1 1
T
 
  
 

(b) Transform the matrix of the system to the reduced row echelon...