Fsc Part 1 Mathematics (Complete Solution)

Q4
Find

If  A=
 
1 2 -3
0 -2 0
-2 -2 1
 
  and B=
 
5 -2 5
3 -1 4
-2 1 -2
 
 , then find; 

(i) A12,A22,A32 and lAl

SOLUTION:

Aij=(-1)i+jMij

A12  =  (-1)1+2
 
0 0
-2 1
 
 =(-1)3 (0-0) =0
A22  =  (-1)2+2
 
1 -3
-2 1
 
 =(-1)4 (1-6) =1(-5)=-5
A32  =  (-1)3+2
 
1 -3
0 0
 
 =(-1)5 (0+0) =0

lAl=a12A12+a22A22+a32A32

    =2(0)+(-2)(-5)+(-2)(0)

   =0+10-0

   =10 

(ii) B21,B22,B23 and lBl

SOLUTION:

B21  =  (-1)2+1
 
-2 5
1 -2
 
 =(-1)3 (4-5) =-1(-1)=1
B22  =  (-1)2+2
 
5 5
-2 -2
 
 =(-1)4 (-10+10) =1(0)=0
B23  =  (-1)2+3
 
5 -2
-2 1
 
 =(-1)5 (5-4) =(-1)(1)=-1

lBl=b21B21+b22B22+b23B23

    =2(1)+(-1)(0)+4(-1)

   =3-0-4

   =-1

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