Fsc Part 1 Mathematics (Complete Solution)

Q11
Find

Find A3  if a=
 
1 1 3
5 2 6
-2 -1 -3
 
 

SOLUTION:

A2=A.A

       =
 
1  1 3
5 2 6
-2 -1 -3
 
  x  
 
1 1 3
5 2 6
-2 -1 -3
 
 
       =
 
(1)(1)+(1)(5)+(3)(-2) (1)(1)+(1)(2)+(3)(-1) (1)(3)+(1)(6)+(3)(-3)
(5)(1)+(2)(5)+(6)(-2) (5)(1)+(2)(2)+(6)(-1) (5)(3)+(2)(6)+(6)(-3)
(-2)(1)+(-1)(5)+(-3)(-2) (-2)(1)+(-1)(2)+(-3)(-1) (-2)(3)+(-1)(6)+(-3)(-3)
 
       =
 
1+5-6  1+2-3 3+6-9
5+10-12 5+4-6 15+12-18
-2-5+6 -2-2+3 -6-6+9
 
       =
 
0 0 0
3 3 9
-1 -1 -3
 

A3=A.A2

       =
 
1 1 3
5 2 6
-2 -1 -3
 
  x  
 
0 0 0
3 3 9
-1 -1 -3
 
 
       =
 
0+3-3 0+3-3 0+9-9
0+6-6 0+6-6 0+18-18
0-3+3 0-3+3 0-9+9
 
       =
 
0 0 0
0 0 0
0 0 0
 
   Hence A3    =
 
0 0 0
0 0 0
0 0 0
 
   
   

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