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Exercise - 4.1

Question-1 :-  Evaluate the determinants : determinant

Solution :-
  |A| = -2 - (-20) = -2 + 20 = 18
    

Question-2 :-  Evaluate the determinants: determinant

Solution :-
(i) |A| = cos2θ - (-sin2θ)
        = cos2θ + sin2θ
        = 1

(ii) |B| = (x2 - x + 1)(x + 1) - (x - 1)(x + 1)
         = x3 + x2 - x2 - x + x + 1 - (x2 - 1)
         = x3 + 1 - x2 + 1
         = x3 - x2 + 2
    

Question-3 :-  determinant

Solution :-
        determinant
    

Question-4 :-  determinant

Solution :-
        determinant
    

Question-5 :-  Evaluate the determinants : determinant

Solution :-
(i)        determinant
    
(ii)      determinant
    
(iii)     determinant
    
(iv)    determinant
    

Question-6 :-  determinant

Solution :-
        determinant
    

Question-7 :-  Find values of x, if determinant

Solution :-
(i) 2 - 20 = 2x2 - 24
  -18 + 24 = 2x2
  6 = 2x2
  x2 = 3
  x = ±√3

(ii) 10 - 12 = 5x - 6x
  -2 = -x
   x = 2
    

Question-8 :-  determinant
(A) 6   (B) ±6   (C) -6   (D) 0

Solution :-
  x2 - 36 = 36 - 36
  x2 - 36 = 0
  x2 = 36
  x = ±6
  The correct answer is B.
    
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