Fsc Part 1 Mathematics (Complete Solution)

Q8
Find the values of a and b

If A =
 
1 2
a b
 
and A2 =
 
0
0 0
 
, find the values of a and b.

SOLUTION:

 A =
 
2
a b
 

then

    A2  =  
 
0 0
0
 
A x A  =  
 
0 0
0
 
   
 
2
a b
 
  
 
1 2
a b
 
   =  
 
0 0
0 0
 
   
 
(1)(1)+(2)(a) (1)(2)+(2)(b)
(a)(1)+(b)(a) (a)(2)+(b)(b)
 
   =  
 
0 0
0 0
 
   
 
1+2a 2+2b
a+ab 2a+b2
 
   =  
 
0 0
0 0
 

using definition of equality of matrices, we have

1+2a=0

2a= -1

a= -1/2

and

2+2b=0

2b=-2

b=-1

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