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# RD Sharma Solution for Class 12 Science Mathematics Chapter 5 - Algebra of Matrices

Our RD Sharma Textbook Solutions are considered extremely helpful for solving the tough questions which are asked in the CBSE Class 12 exam. TopperLearning Textbook Solutions are compiled by subject experts. Herein, you can find all the answers to the textbook questions for Chapter 5 - Algebra of Matrices.

All our solutions are created in accordance with the latest CBSE syllabus, and they are amended from time to time to provide the most relevant answers. Our free RD Sharma Solutions for CBSE Class 12 Mathematics will strengthen your fundamentals in Mathematics and will help you in your attempts to score more marks in the final examination. CBSE Class 12 students can refer to our solutions any time — while doing their homework and while preparing for the exam.

Exercise/Page

## RD Sharma Solution for Class 12 Science Mathematics Chapter 5 - Algebra of Matrices Page/Excercise 5.1

Solution 1

We know that if a matrix is of the order , it has mn elements. Thus, to find all the possible orders of a matrix having 8 elements, we have to find all the ordered pairs of natural numbers whose products is 8.

The ordered pairs are:

are the ordered pairs of natural numbers whose product is 5.

Hence, the possible orders of a matrix having 5 elements are

Solution 2

Solution 3

Solution 4

Solution 5

Solution 5(vii)

Solution 6

(v)

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 1

Solution 2(i)

Solution 2(ii)

Solution 2(iii)

Solution 2(iv)

Solution 3

(ii)

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15(i)

Solution 15(ii)

Solution 15(iii)

Solution 16

Solution 17

Solution 18

(i)

(ii)

Solution 19(i)

Solution 19(ii)

Solution 20

Solution 21

## RD Sharma Solution for Class 12 Science Mathematics Chapter 5 - Algebra of Matrices Page/Excercise 5.3

Solution 1

Solution 2(i)

Solution 2(ii)

Solution 2(iii)

Solution 3(i)

Solution 3(ii)

Solution 3(iii)

Solution 3(iv)

Solution 4(i)

Solution 4(ii)

Solution 5(i)

Solution 5(ii)

Solution 5(iii)

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16(i)

Solution 16(ii)

Solution 17(i)

Solution 17(ii)

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Solution 24(i)

Solution 24(ii)

Solution 25

Solution 26

Solution 27

Solution 28

Solution 29

Solution 30

Solution 31

Solution 32

Solution 33

Solution 34

Solution 35

Solution 36

Solution 37

Solution 38

Solution 39

Solution 40(i)

Solution 40(ii)

Solution 40(iii)

Solution 41

Solution 42

Solution 43

Solution 44

Solution 45

Solution 46

Solution 47

Solution 48(i)

Solution 48(ii)

Solution 48(iii)

Solution 48(iv)

Solution 49

Solution 50

So,

A16 is null matrix.

Solution 51

Solution 52

Solution 53

Solution 54(i)

Solution 54(ii)

Solution 55

Solution 56

Solution 57

Solution 58

Solution 59

Solution 60

Solution 61

Solution 62

Solution 64

Solution 65(i)

Solution 65(ii)

Solution 65(iii)

Solution 65(iv)

Solution 66

Solution 67

Solution 68

Solution 69

Solution 70

Solution 71

Solution 72

Solution 73

Solution 74

Solution 75

Solution 76

Solution 77

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 1(iv)

Solution 2

Solution 3(i)

Solution 3(ii)

Solution 3(iii)

Solution 4

Solution 5

Solution 6(i)

Solution 6(ii)

Solution 7

Solution 8

Solution 9

Solution 10

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

## RD Sharma Solution for Class 12 Science Mathematics Chapter 5 - Algebra of Matrices Page/Excercise MCQ

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Solution 24

Solution 25

Solution 26

Solution 27

Solution 28

Solution 29

Solution 30

Solution 31

Solution 32

Solution 33

Solution 34

Solution 35

Solution 36

Solution 37

Solution 38

Solution 39

Solution 40

Solution 41

Solution 42

Solution 43

Solution 44

Solution 45

Correct option: (d)

A matrix is called Diagonal matrix if all the elements, except those in the leading diagonal, are zero.

## RD Sharma Solution for Class 12 Science Mathematics Chapter 5 - Algebra of Matrices Page/Excercise 5VSAQ

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Solution 24

Solution 25

Solution 26

Solution 27

Solution 28

Solution 29

Solution 30

Solution 31

Solution 32

Solution 33

Solution 34

Solution 35

Solution 36

Solution 37

Solution 38

Solution 39

Solution 40

Solution 41

Solution 42

Solution 43

Solution 44

Solution 45

Solution 46

Solution 47

Solution 48

Solution 49

If a matrix is of order , then the number of elements in the matrix is the product .

Given that the required matrix is having 5 elements and 5 is a prime number.

Hence the prime factorization of 5 is either .

Thus, the order of the matrix is either .

Solution 50

Solution 51

Solution 52

Solution 53

Solution 54

Solution 55

Solution 56

A2 = A

A3 = A2 = A

7A - (I + A)3

= 7A - (I3 + A3 + 3A2I + 3AI2)

= 7A - (I + A + 3A + 3A)

= 7A - (I + 7A)

= -I

Solution 57

Solution 58

Solution 59

Solution 60

Solution 61

Solution 62

Solution 63

## Browse Study Material

TopperLearning provides step-by-step solutions for each question in each chapter in the RD Sharma textbook for class 9. Access the CBSE Class 9 Mathematics Chapter 5 - Algebra of Matrices for free. The textbook questions have been solved by our subject matter experts to help you understand how to answer them. Our RD Sharma Textbook Solutions will help you to study and revise, and you can easily clear your fundamentals of Chapter 5 - Algebra of Matrices.

# Text Book Solutions

CBSE XII Science - Mathematics

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