NCERT Solutions for Class 12 Maths Chapter 3 Matrices — Exercise 3.3

ncert class 12 maths chapter 3 Matrices

Question 1:Find the transpose of each of the following matrices: (i) 5 1 2 1
       −    (ii) 1 1 2 3
−      (iii) 1 5 6 3 5 6 2 3 1
−       −   

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Question 2:If 1 2 3 4 1 5 A 5 7 9 and B 1 2 0 2 1 1 1 3 1
− 
− −      =   =   −    , then verify that (i) (A + B)¢ = A¢ + B¢, (ii) (A – B)¢ = A¢ – B¢

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Question 3:If 3 4 1 2 1 A 1 2 and B 1 2 3 0 1
  
−  ¢ = −  =         , then verify that (i) (A + B)¢ = A¢ + B¢ (ii) (A – B)¢ = A¢ – B¢

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Question 4:If 2 3 1 0 A and B 1 2 1 2
− 
−  ¢ =   =       , then find (A + 2B)¢

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Question 5:For the matrices A and B, verify that (AB)¢ = B¢A¢, where (i) [ ] 1 A 4 , B 1 2 1 3
   = −  = −   (ii) [ ] 0 A 1 , B 1 5 7 2
   =   =  

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Question 6:If (i) cos sin A sin cos
a a =   − a a , then verify that A¢ A = I (ii) If sin cos A cos sin
a a =   − a a , then verify that A¢ A = I

Question 7:(i) Show that the matrix 1 1 5 A 1 2 1 5 1 3
−    = −     is a symmetric matrix. (ii) Show that the matrix 0 1 1 A 1 0 1 1 1 0
−    = −   −  is a skew symmetric matrix.

Exercise 3.3 class 12 Math ncert solutions Chapter 3

Question 8:For the matrix 1 5 A 6 7
 =     , verify that (i) (A + A¢) is a symmetric matrix (ii) (A – A¢) is a skew symmetric matrix

1. Find the transpose of each of the following mat

Question 9:Find ( ) 1 A A 2 + ¢ and ( ) 1 A A 2 − ¢ , when 0 A 0 0 a b a c b c
   = −  − − 

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Question 10:Express the following matrices as the sum of a symmetric and a skew symmetric matrix: (i) 3 5 1 1
    −  (ii) 6 2 2 2 3 1 2 1 3
−    − −   −  (iii) 3 3 1 2 2 1 4 5 2
−    − −  − −  (iv) 1 5 1 2
   −  Choose the correct answer in the Exercises 11 and 12

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Question 11:If A, B are symmetric matrices of same order, then AB – BA is a (A) Skew symmetric matrix (B) Symmetric matrix (C) Zero matrix (D) Identity matrix

Question 12:If cos sin A , sin cos
a − a  =    a a and A + A¢ = I, then the value of a is (A) 6 p (B) 3 p (C) π (D) 3 2 p