NCERT Solutions for Class 12 Maths Chapter 3 Matrices — Exercise 3.2

Question 1:Let 2 4 1 3 2 5 A , B , C 3 2 2 5 3 4


−  =   =   =     −    Find each of the following: (i) A + B (ii) A – B (iii) 3A – C (iv) AB (v) BA

Question 2:Compute the following: (i) a b a b b a b a

   +   −     (ii) 2 2 2 2 2 2 2 2 2 2 2 2 a b b c ab bc a c a b ac ab
+ + 
   +    + +  − −  (iii) 1 4 6 12 7 6 8 5 16 8 0 5 2 8 5 3 2 4
− − 
       +       (iv) 2 2 2 2 2 2 2 2 cos sin sin cos sin cos cos sin x x x x x x x x

   +      

ncert class 12 maths chapter 3 Matrices

Question 3:Compute the indicated products. (i) a b a b b a b a

−      −     (ii) 1 2 3
       [2 3 4] (iii) 1 2 1 2 3 2 3 2 3 1
− 
         (iv) 2 3 4 1 3 5 3 4 5 0 2 4 4 5 6 3 0 5

−              (v) 2 1 1 0 1 3 2 1 2 1 1 1
  
     −  −  (vi) 2 3 3 1 3 1 0 1 0 2 3 1
− 
−        −   

exercise 3.2 maths class 12 Chapter 3 Matrices

Question 4:If 1 2 3 3 1 2 4 1 2 A 5 0 2 , B 4 2 5 and C 0 3 2 1 1 1 2 0 3 1 2 3
− 
− 
       =   =   =    −     −  , then compute (A+B) and (B – C). Also, verify that A + (B – C) = (A + B) – C.

Question 5:If 2 5 2 3 1 1 3 3 5 5 1 2 4 1 2 4 A and B 3 3 3 5 5 5 7 2 7 6 2 2 3 3 5 5 5

             =   =               , then compute 3A – 5B.

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Question 6:Simplify cos sin sin cos cos + sin sin cos cos sin
q q
q − q q   q   − q q  q q

Class 12 maths solutions Matrices

Question 7:Find X and Y, if (i) 7 0 3 0 X + Y and X – Y 2 5 0 3

 =   =       (ii) 2 3 2 2 2X + 3Y and 3X 2Y 4 0 1 5

−  =   + =     − 

Question 8:Find X, if Y = 3 2 1 4
     and 2X + Y = 1 0 3 2
   − 

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Question 9:Find x and y, if 1 3 0 5 6 2 0 1 2 1 8 y x


   +   =        

Matrices Class 12 ncert solutions

Question 10:Solve the equation for x, y, z and t, if 1 1 3 5 2 3 3 0 2 4 6 x z y t

− 
   +   =        

Question 11:If 2 1 10 3 1 5 x y

− 
   +   =         , find the values of x and y.

Question 12:Given 6 4 3 1 2 3 x y x x y z w w z w


+    =   +     −   +  , find the values of x, y, z and w.

Question 13:If cos sin 0 F ( ) sin cos 0 0 0 1 x x x x x
−    =     , show that F(x) F(y) = F(x + y).

Exercise 3.2 class 12 Math ncert solutions Chapter 3

Question 14:Show that (i) 5 1 2 1 2 1 5 1 6 7 3 4 3 4 6 7
− 


−      ¹             (ii) 1 2 3 1 1 0 1 1 0 1 2 3 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 2 3 4 2 3 4 1 1 0

− 
− 
            −  ¹  −           

1. Let 2 4 1 3 2 5 A , B , C 3 2 2 5 3 4

Question 15:Find A2 – 5A + 6I, if 2 0 1 A 2 1 3 1 1 0
   =    − 

Question 16:If 1 0 2 A 0 2 1 2 0 3
   =     , prove that A3 – 6A2 + 7A + 2I = 0

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Question 17:If 3 2 1 0 A and I= 4 2 0 1
− 
 =      −    , find k so that A2 = kA – 2I

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Question 18:If 0 tan 2 A tan 0 2
a  −  =    a    and I is the identity matrix of order 2, show that I + A = (I – A) cos sin sin cos
a − a    a a

Question 19:A trust fund has ` 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide ` 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of: (a) ` 1800 (b) ` 2000

Matrices ncert solutions class 12

Question 20:The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are ` 80, ` 60 and ` 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra. Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and π × k, respectively. Choose the correct answer in Exercises 21 and 22

CBSE NCERT Solutions For Class 12 Matrices

Question 21:The restriction on n, k and π so that PY + WY will be defined are: (A) k = 3, π = n (B) k is arbitrary, π = 2 (C) π is arbitrary, k = 3 (D) k = 2, π = 3

Question 22:If n = p, then the order of the matrix 7X – 5Z is: (A) π × 2 (B) 2 × n (C) n × 3 (D) π × n