Fsc Part 1 Mathematics (Complete Solution)

Q1
Show that A+B is symmetric

If  A=
 
1 -2 5
-2 3 -1
5 -1 0
 
  and  B= 
 
-3 1 -2
1 0 -1
-2 -1 2
 
  then show that A+B is symmetric. 

SOLUTION:

  A+B =  
 
1 -2 5
-2 3 -1
5 -1 0
 
  + 
 
-3 1 -2
1 0 -1
-2 -1 2
 
 
       =  
 
-2 -1 3
-1 3 -2
3 -2 2
 
      (A+B)t =  
 
-2 -1 3
-1 3 -2
3 -2 2
 

=A+B

Hence (A+B) is symmetric Matrix

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