Selina Concise Mathematics Class 10 ICSE Solutions Matrices

Selina Concise Mathematics Class 10 ICSE Solutions Matrices

Selina Publishers Concise Mathematics Class 10 ICSE Solutions Chapter 9 Matrices

Matrices Exercise 9A – Selina Concise Mathematics Class 10 ICSE Solutions

Question 1.
State, whether the following statements are true or false. If false, give a reason.
(i) If A and B are two matrices of orders 3 × 2 and 2 × 3 respectively; then their sum A + B is possible.
(ii) The matrices A2 × 3 and B2 × 3 are conformable for subtraction.
(iii) Transpose of a 2 × 1 matrix is a 2 × 1 matrix.
(iv) Transpose of a square matrix is a square matrix.
(v) A column matrix has many columns and one row.
Solution:
(i) False
The sum A + B is possible when the order of both the matrices A and B are same.
(ii) True
(iii) False
Transpose of a 2 1 matrix is a 1 2 matrix.
(iv) True
(v) False
A column matrix has only one column and many rows.

Question 2.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices - 1
Solution:
If two matrices are equal, then their corresponding elements are also equal. Therefore, we have:
x = 3,
y + 2 = 1 ⇒ y = -1
z – 1 = 2 ⇒ z = 3

Question 3.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 2
Solution:
If two matrices are equal, then their corresponding elements are also equal.
(i)
a + 5 = 2 ⇒ a = -3
-4 = b + 4 ⇒ b = -8
2 = c – 1 ⇒ c = 3
(ii) a= 3
a – b = -1
⇒ b = a + 1 = 4
b + c = 2
⇒ c = 2 – b = 2 – 4 = -2

Question 4.
If A = [8  -3] and B = [4  -5]; find: (i) A + B (ii) B – A
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 3

Question 5.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 4
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 5

Question 6.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 6
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 7

Question 7.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 8
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 9

Question 8.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 10
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 11

Question 9.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 12
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 13

Question 10.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 14
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 15

Question 11.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 16
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 17

Matrices Exercise 9B – Selina Concise Mathematics Class 10 ICSE Solutions

Question 1.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 18
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 19

Question 2.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 20
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 21

Question 3.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 22
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 23

Question 4.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 24
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 25

Question 5.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 26
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 27

Question 6.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 28
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 29

Question 7.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 30
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 31
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 32

Question 8.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 33
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 34

Question 9.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 35
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 36

Question 10.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 37
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 38

Question 11.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 39
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 40

Matrices Exercise 9C – Selina Concise Mathematics Class 10 ICSE Solutions

Question 1.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 41
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 42
The number of columns in the first matrix is not equal to the number of rows in the second matrix. Thus, the product is not possible.

Question 2.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 43
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 44
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 45

Question 3.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 46
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 47

Question 4.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 48
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 49

Question 5.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 50
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 51

Question 6.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 52
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 53
(iii) Product AA (=A2) is not possible as the number of columns of matrix A is not equal to its number of rows.

Question 7.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 54
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 55

Question 8.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 56
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 57

Question 9.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 58
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 59

Question 10.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 60
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 61

Question 11.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 149
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 63

Question 12.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 64
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 65

Question 13.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 66
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 67

Question 14.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 68
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 69

Question 15.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 70
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 71

Question 16(i).
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 72
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 73

Question 16(ii).
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 74
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 75

Question 16(iii).
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 76
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 77

Question 17.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 78
Solution:
We know, the product of two matrices is defined only when the number of columns of first matrix is equal to the number of rows of the second matrix.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 79
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 80

Question 18.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 81
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 82

Question 19.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 83
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 84

Question 20.
If A and B are any two 2 x 2 matrices such that AB = BA = B and B is not a zero matrix, what can you say about the matrix A?
Solution:
AB = BA = B
We know that AI = IA = I, where I is the identity matrix.
Hence, B is the identity matrix.

Question 21.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 85
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 86

Question 22.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 87
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 88

Question 23.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 89
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 90

Question 24.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 91
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 92

Question 25.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 93
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 94

Question 26.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 95
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 96

Question 27.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 97
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 98

Question 28.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 99
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 100

Question 29.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 101
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 102

Question 30.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 103
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 104

Question 31.
State, with reason, whether the following are true or false. A, B and C are matrices of order 2 x 2.
(i) A + B = B + A
(ii) A – B = B – A
(iii) (B. C). A = B. (C. A)
(iv) (A + B). C = A. C + B. C
(v) A. (B – C) = A. B – A. C
(vi) (A – B). C = A. C – B. C
(vii) A² – B² = (A + B) (A – B)
(viii) (A – B)² = A² – 2A. B + B²
Solution:
(i) True.
Addition of matrices is commutative.
(ii) False.
Subtraction of matrices is commutative.
(iii) True.
Multiplication of matrices is associative.
(iv) True.
Multiplication of matrices is distributive over addition.
(v) True.
Multiplication of matrices is distributive over subtraction.
(vi) True.
Multiplication of matrices is distributive over subtraction.
(vii) False.
Laws of algebra for factorization and expansion are not applicable to matrices.
(viii) False.
Laws of algebra for factorization and expansion are not applicable to matrices.

Matrices Exercise 9D – Selina Concise Mathematics Class 10 ICSE Solutions

Question 1.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 105
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 106

Question 2.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 107
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 108

Question 3.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 109
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 111

Question 4.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 112
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 113
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 114

Question 5.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 115
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 116

Question 6.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 117
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 118

Question 7.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 119
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 120

Question 8.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 121
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 122

Question 9.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 123
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 124

Question 10.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 125
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 126

Question 11.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 127
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 128

Question 12.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 129
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 130

Question 13.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 131
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 132

Question 14.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 133
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 134

Question 15.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 135
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 136

Question 16.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 137
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 138

Question 17.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 139
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 140

Question 18.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 141
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 142

Question 19.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 143
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 144

Question 20.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 145
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 146

Question 21.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 147
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices image - 148

Question 22.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices ex 9d q22
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices ex 9d q22

Question 23.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices ex 9d q23
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices ex 9d q23
Selina Concise Mathematics Class 10 ICSE Solutions Matrices ex 9d q23.1

Question 24.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices ex 9d q24
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices ex 9d q24

Question 25.
Selina Concise Mathematics Class 10 ICSE Solutions Matrices ex 9d q25
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Matrices ex 9d q25

More Resources for Selina Concise Class 10 ICSE Solutions

ICSE Solutions Selina ICSE Solutions