NCERT Solutions for Class 12 Maths Chapter 4 Determinants — Exercise 4.2

Question 1:0 x a x a y b y b z c z c + + = +

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Question 2:0 a b b c c a b c c a a b c a a b b c − − − − − − = − − −

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Question 3:2 7 65 3 8 75 0 5 9 86 =

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Question 4:( ) ( ) ( ) 1 1 0 1 bc a b c ca b c a ab c a b + + = +

Question 5:2 b c q r y z a π x c a r π z x b q y a b π q x y c r z

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Question 6:0 0 0 0 a b a c b c − − − =

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Question 7:2 2 2 2 2 2 4 a ab ac ba b bc a b c ca cb c − − = − By using properties of determinants, in Exercises 8 to 14, show that:

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Question 8:(i) ( )( )( ) 2 2 2 1 1 1 a a b b a b b c c a c c = − − − (ii) ( )( )( )( ) 3 3 3 1 1 1 a b c a b b c c a a b c a b c = − − − + +

Question 9:2 2 2 x x yz y y zx z z xy = (x – y) (y – z) (z – x) (xy + yz + zx)

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Question 10:(i) ( )( )2 4 2 2 2 4 5 4 4 2 2 4 x+ x x x x+ 2x x x x x x+ = + − (ii) ( ) 2 3 y+k y y y y+k y k y k y y y+k = +

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Question 11:(i) ( )3 2 2 2 2 2 2 a b c a a b b c a b a b c c c c a b − − − − = + + − − (ii) ( )3 2 2 2 2 x y z x y z y z x y x y z z x z x y

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Question 12:( ) 2 2 2 3 2 1 1 1 1 x x x x x x x = −

Question 13:( ) 2 2 3 2 2 2 2 2 2 1 2 2 2 1 2 1 2 2 1 a b ab b ab a b a a b b a a b + − − − + = + + − − −

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Question 14:2 2 2 2 2 2 1 1 1 1 a ab ac ab b bc a b c ca cb c + + = + + + + Choose the correct answer in Exercises 15 and 16

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Question 15:Let A be a square matrix of order 3 × 3, then | kA| is equal to (A) k|A| (B) k2 | A | (C) k3 | A | (D) 3k | A |

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Question 16:Which of the following is correct (A) Determinant is a square matrix. (B) Determinant is a number associated to a matrix. (C) Determinant is a number associated to a square matrix. (D) None of these