Fsc Part 1 Mathematics (Complete Solution)

Q4
Find the following matrices

if A =
 
-1 2 3
1 0 2
 
and B =
 
0 3 2
1 -1 2
 
,find the following matrices;

(i) 4A-3B

SOLUTION:   4A-3B

       =  4
 
-1 2 3
1 0 2
 
  -  3 
 
0 3 2
1 -1 2
 
 
       =  
 
-4 8 12
4 0 8
 
  -   
 
0 9 6
3 -3 6
 
 
       =  
 
-4-0 8-9 12-6
4-3 0+3 8-6
 
       =  
 
-4 -1 6
1 3 2
 

(ii) A+3(B-A)

SOLUTION:   A+3(B-A)

 => B-A      =  
 
3 2
1 -1 2
 
  -   
 
-1  2 3
1 0 2
 
 
       =  
 
0+1  3-2 2-3
1-1 -1-0 2-2
 
       =  
 
1 -1
0 -1 0
 

then

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

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