Fsc Part 1 Mathematics (Complete Solution)

Q10
Show that

If A =
 
1 -1 2
0 1
 
and B =
 
2 3 0
1 2 -1
 
, then show that (A+B)t=At+Bt.

SOLUTION:

      A =
 
-1 2
0 3 1
 
  =>    At =
 
0
-1 3
2 1
 
      B =
 
2 3 0
1 2 -1
 
 =>     Bt =
 
2 1
3 2
0 -1
 
 => A+B=  
 
1 -1 2
0 3 1
 
 + 
 
3 0
1 2 -1
 
   =  
 
3 2 2
1 5 0
 

        Given (A+B)t=At+Bt

L.H.S=(A+B)t

   =
 
1
2 5
2 0
 

R.H.S=At+Bt

       =         
 
1 0
-1 3
2 1
 
  + 
 
2 1
3 2
0 -1
 
 
          =
 
3 1
2 5
2 0
 

L.H.S=R.H.S

Hence   (A+B)t=At+Bt

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