RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix

The RD Sharma textbook contains a huge number of solved examples and illustrations. It also provides quality content, easy stepwise explanations of various difficult concepts and a wide variety of questions for practice. RD Sharma Solutions are completely based on the exam-oriented approach to help the students in board exams. The PDF of RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix is provided here.

Practising these questions will ensure that they can easily excel in their final examination for the subject of Mathematics. Students can refer and download Chapter 7 Adjoint and Inverse of a Matrix from the given links. This chapter is based on the adjoint of a square matrix and its properties. RD Sharma Solutions cover all the topics related to it. Some of the essential topics of this chapter are listed below.

  • Definition and meaning of adjoint of a square matrix
  • The inverse of a matrix
  • Some useful results on invertible matrices
  • Determining the adjoint and inverse of a matrix
  • Determining the inverse of a matrix when it satisfies the matrix equation
  • Finding the inverse of a matrix by using the definition of inverse
  • Finding a non – singular matrix when adjoint is given
  • Elementary transformation or elementary operations of a matrix
  • Method of finding the inverse of a matrix by elementary transformation

RD Sharma Solutions For Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix:-Download PDF Here

RD Sharma Class 12 Maths Solutions Chapter 7 Adjoint And Inverse Of A Matrix
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Access answers to Maths RD Sharma Solutions For Class 12 Chapter 7 – Adjoint and Inverse of a Matrix

Exercise 7.1 Page No: 7.22

1. Find the adjoint of each of the following matrices:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 1
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 2
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 3
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 4

Verify that (adj A) A = |A| I = A (adj A) for the above matrices.

Solution:

(i) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 5

Cofactors of A are

C11 = 4

C12 = – 2

C21 = – 5

C22 = – 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 6
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 7

(ii) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 8

Therefore cofactors of A are

C11 = d

C12 = – c

C21 = – b

C22 = a

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 9
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 10

(iii) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 11

Therefore cofactors of A are

C11 = cos α

C12 = – sin α

C21 = – sin α

C22 = cos α

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 12
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 13

(iv) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 14

Therefore cofactors of A are

C11 = 1

C12 = tan α/2

C21 = – tan α/2

C22 = 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 15
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 16

2. Compute the adjoint of each of the following matrices.

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 17
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 18

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 19
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 20

Solution:

(i) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 21

Therefore cofactors of A are

C11 = – 3

C21 = 2

C31 = 2

C12 = 2

C22 = – 3

C23 = 2

C13 = 2

C23 = 2

C33 = – 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 22
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 23

(ii) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 24

Cofactors of A

C11 = 2

C21 = 3

C31 = – 13

C12 = – 3

C22 = 6

C32 = 9

C13 = 5

C23 = – 3

C33 = – 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 25
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 26
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 27

(iii) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 28

Therefore cofactors of A

C11 = – 22

C21 = 11

C31 = – 11

C12 = 4

C22 = – 2

C32 = 2

C13 = 16

C23 = – 8

C33 = 8

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 29
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 30
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 31
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 32

(iv) Let

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 33

Therefore cofactors of A

C11 = 3

C21 = – 1

C31 = – 1

C12 = – 15

C22 = 7

C32 = – 5

C13 = 4

C23 = – 2

C33 = 2

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 34
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 35

Hence, (adj A) A = |A|I = A(adj A)

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 36

Solution:

Given

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 37

Therefore cofactors of A

C11 = 30

C21 = 12

C31 = – 3

C12 = – 20

C22 = – 8

C32 = 2

C13 = – 50

C23 = – 20

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 38
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 39
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 40

Solution:

Given

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 41

Cofactors of A

C11 = – 4

C21 = – 3

C31 = – 3

C12 = 1

C22 = 0

C32 = 1

C13 = 4

C23 = 4

C33 = 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 42
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 43

Solution:

Given

A = RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 44

Cofactors of A are

C11 = – 3

C21 = 6

C31 = 6

C12 = – 6

C22 = 3

C32 = – 6

C13 = – 6

C23 = – 6

C33 = 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 45
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 46

Solution:

Given

A = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 47

Cofactors of A are

C11 = 9

C21 = 19

C31 = – 4

C12 = 4

C22 = 14

C32 = 1

C13 = 8

C23 = 3

C33 = 2

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 48
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 49

7. Find the inverse of each of the following matrices:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 50
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 51
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 52
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 53

Solution:

(i) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

Now, |A| = cos θ (cos θ) + sin θ (sin θ)

= 1

Hence, A – 1 exists.

Cofactors of A are

C11 = cos θ

C12 = sin θ

C21 = – sin θ

C22 = cos θ

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 54
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 55

(ii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

Now, |A| = – 1 ≠ 0

Hence, A – 1 exists.

Cofactors of A are

C11 = 0

C12 = – 1

C21 = – 1

C22 = 0

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 56

(iii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 57
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 58

(iv) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

Now, |A| = 2 + 15 = 17

Hence, A – 1 exists.

Cofactors of A are

C11 = 1

C12 = 3

C21 = – 5

C22 = 2

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 59

8. Find the inverse of each of the following matrices.

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RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 61
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RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 65
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 66

Solution:

(i) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 67

= 1(6 – 1) – 2(4 – 3) + 3(2 – 9)

= 5 – 2 – 21

= – 18

Hence, A – 1 exists

Cofactors of A are

C11 = 5

C21 = – 1

C31 = – 7

C12 = – 1

C22 = – 7

C32 = 5

C13 = – 7

C23 = 5

C33 = – 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 68
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 69

(ii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 70

= 1 (1 + 3) – 2 (– 1 + 2) + 5 (3 + 2)

= 4 – 2 + 25

= 27

Hence, A – 1 exists

Cofactors of A are

C11 = 4

C21 = 17

C31 = 3

C12 = – 1

C22 = – 11

C32 = 6

C13 = 5

C23 = 1

C33 = – 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 71
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 72

(iii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 73

= 2(4 – 1) + 1(– 2 + 1) + 1(1 – 2)

= 6 – 2

= – 4

Hence, A – 1 exists

Cofactors of A are

C11 = 3

C21 = 1

C31 = – 1

C12 = + 1

C22 = 3

C32 = 1

C13 = – 1

C23 = 1

C33 = 3

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 74

(iv) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 75

= 2(3 – 0) – 0 – 1(5)

= 6 – 5

= 1

Hence, A – 1 exists

Cofactors of A are

C11 = 3

C21 = – 1

C31 = 1

C12 = – 15

C22 = 6

C32 = – 5

C13 = – 5

C23 = – 2

C33 = 2

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 76

(v) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 77

= 0 – 1 (16 – 12) – 1 (– 12 + 9)

= – 4 + 3

= – 1

Hence, A – 1 exists

Cofactors of A are

C11 = 0

C21 = – 1

C31 = 1

C12 = – 4

C22 = 3

C32 = – 4

C13 = – 3

C23 = 3

C33 = – 4

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 78

(vi) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 79

= 0 – 0 – 1(– 12 + 8)

= 4

Hence, A – 1 exists

Cofactors of A are

C11 = – 8

C21 = 4

C31 = 4

C12 = 11

C22 = – 2

C32 = – 3

C13 = – 4

C23 = 0

C33 = 0

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 80

(vii) The criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 81 – 0 + 0

= – (cos2 α – sin2 α)

= – 1

Hence, A – 1 exists

Cofactors of A are

C11 = – 1

C21 = 0

C31 = 0

C12 = 0

C22 = – cos α

C32 = – sin α

C13 = 0

C23 = – sin α

C33 = cos α

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 82

9. Find the inverse of each of the following matrices and verify that A-1A = I3.

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 83
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 84

Solution:

(i) We have

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 85

= 1(16 – 9) – 3(4 – 3) + 3(3 – 4)

= 7 – 3 – 3

= 1

Hence, A – 1 exists

Cofactors of A are

C11 = 7

C21 = – 3

C31 = – 3

C12 = – 1

C22 = – 1

C32 = 0

C13 = – 1

C23 = 0

C33 = 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 86
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 87
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 88

(ii) We have

|A| = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 89

= 2(8 – 7) – 3(6 – 3) + 1(21 – 12)

= 2 – 9 + 9

= 2

Hence, A – 1 exists

Cofactors of A are

C11 = 1

C21 = 1

C31 = – 1

C12 = – 3

C22 = 1

C32 = 1

C13 = 9

C23 = – 5

C33 = – 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 90
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 91

10. For the following pair of matrices verify that (AB)-1 = B-1A-1.

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 92
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 93

Solution:

(i) Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 94
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 95

(ii) Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 96
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 97
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 98

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 99
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 100
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 101

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 102
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 103
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 104

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 105
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 106
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 107

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 108
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 109
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 110
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 111

Solution:

Given

A = 
https://gradeup-question-images.grdp.co/liveData/PROJ23872/1543574054891449.png and B – 1 = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 113

Here, (AB) – 1 = B – 1 A – 1

|A| = – 5 + 4 = – 1

Cofactors of A are

C11 = – 1

C21 = 8

C31 = – 12

C12 = 0

C22 = 1

C32 = – 2

C13 = 1

C23 = – 10

C33 = 15

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 114
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 115

(i) [F (α)]-1 = F (-α)

(ii) [G (β)]-1 = G (-β)

(iii) [F (α) G (β)]-1 = G (-β) F (-α)

Solution:

(i) Given

F (α) = 
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 116

|F (α)| = cos2 α + sin2 α = 1

Cofactors of A are

C11 = cos α

C21 = sin α

C31 = 0

C12 = – sin α

C22 = cos α

C32 = 0

C13 = 0

C23 = – 10

C33 = 1

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 117
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 118

(ii) We have

|G (β)| = cos2 β + sin2 β = 1

Cofactors of A are

C11 = cos β

C21 = sin α

C31 = sin β

C12 = 0

C22 = 1

C32 = 0

C13 = sin β

C23 = 0

C33 = cos β

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 119
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 120

(iii) Now we have to show that

[F (α) G (β)] – 1 = G (– β) F (– α)

We have already know that

[G (β)] – 1 = G (– β)

[F (α)] – 1 = F (– α)

And LHS = [F (α) G (β)] – 1

= [G (β)] – 1 [F (α)] – 1

= G (– β) F (– α)

Hence = RHS

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 121

Solution:

Consider,

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 122
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 123
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 124

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 125
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 126
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 127
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 128

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 129
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 130

Exercise 7.2 Page No: 7.34

Find the inverse of the following matrices by using elementary row transformations:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 131

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 132
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 133
134

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 135
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 136
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 137

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 138
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 139
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 140

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 141
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 142
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 143

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 144
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 145
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 146

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 147
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 148
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 149
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 150

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 151
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 152
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 153
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 154

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 155
RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix Image 156

Also, access RD Sharma Solutions for Class 12 Maths Chapter 7 Adjoint and Inverse of a Matrix

Exercise 7.1 Solutions

Exercise 7.2 Solutions

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