NCERT Solutions For Class 12 Maths Chapter 4 Determinants Exercise 4.5 Question 1 to 18 Answer: Downlaod pdf

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Find adjoint of each of the matrices in Exercises 1 and 2

Question 1:1 2 3 4 é ë ê ù û ú

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Question 2:1 1 2 2 3 5 2 0 1 − − é ë êêê ù û úúú Verify A (adj A) = (adj A) A = |A| I in Exercises 3 and 4

Question 3:2 3 −4 −6 é ë ê ù û ú

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Question 4:1 1 2 3 0 2 1 0 3 − − é ë êêê ù û úúú Find the inverse of each of the matrices (if it exists) given in Exercises 5 to 11

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Question 5:2 2 4 3 é − ë ê ù û ú

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Question 6:− − é ë ê ù û ú 1 5 3 2

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Question 7:1 2 3 0 2 4 0 0 5 é ë êêê ù û úúú

Question 8:1 0 0 3 3 0 5 2 −1 é ë êêê ù û úúú

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Question 9:2 1 3 4 1 0 7 2 1 − − é ë êêê ù û úúú

Question 10:1 1 2 0 2 3 3 2 4 − − − é ë êêê ù û úúú

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Question 11:1 0 0 0 cos sin 0 sin cos
    a a   a − a

Question 12:Let A = 3 7 2 5 é ë ê ù û ú and B = 6 8 7 9 é ë ê ù û ú . Verify that (AB)–1 = B–1 A–1.

Find adjoint of each of the matrices in Exercises

Question 13:If A = 3 1 −1 2 é ë ê ù û ú , show that A2 – 5A + 7I = O. Hence find A–1.

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Question 14:For the matrix A = 3 2 1 1 é ë ê ù û ú , find the numbers a and b such that A2 + aA + bI = O.

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Question 15:For the matrix A = 1 1 1 1 2 3 2 1 3 − − é ë êêê ù û úúú Show that A3– 6A2 + 5A + 11 I = O. Hence, find A–1.

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Question 16:If A = 2 1 1 1 2 1 1 1 2 − − − − é ë êêê ù û úúú Verify that A3 – 6A2 + 9A – 4I = O and hence find A–1

Question 17:Let A be a nonsingular square matrix of order 3 ×

Question 3:Then |adj A| is equal to (A) |A | (B) | A|2 (C) | A|3 (D) 3|A|

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Question 18:If A is an invertible matrix of order 2, then det (A–1) is equal to (A) det (A) (B) 1 det (A) (C) 1 (D) 0

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