Fsc Part 1 Mathematics (Complete Solution)

Q11
Find the value of λ if A and B are singular.

A =
 
4 λ 3
7 3 6
2 3 1
 
 ,  B=
 
5 1 2 0
8 2 5 1
3 2 0 1
2 λ -1 3
 
 

SOLUTION:  (i)

lAl =  
 
4 λ 3
7 3 6
2 3 1
 

= 4(3-18)-λ(7-12)+3(21-6)

=-60+5λ+45

=5λ-15

for singular lAl=0

5λ-15=0

5λ=15

=> λ=3

(ii)

lBl =
 
5 1 2 0
8 2 5 1
3 2 0 1
2 λ -1 3
 
  
      = 
 
0 0 0
-2 2 1 1
-7 2 4 1
2-5λ λ -1-2λ 3
 
  C1-5C2
  C3-2C2
      =1(-1)1+2 
 
-2 1 1
-7 4 1
2-5λ -1-2λ 3
 
  
      = -1  
 
0 0 1
-5 -5 1
8-5λ -4-2λ 3
 
  C1+2C3
  C2-C3
      = (-1)(1) 
 
-5 -5
8-5λ -4-2λ
 
  

=  -(20+10λ+40-25λ)

=15λ-60

For singular lBl=0

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