ML Aggarwal Solutions for Class 10 Maths Chapter 8 Matrices

ML Aggarwal Solutions For Class 10 Maths Chapter 8 Matrices consists of accurate solutions, which help the students to quickly complete their homework and prepare well for the exams. These Solutions of ML Aggarwal provide students an advantage with practical questions. Each step in the solution is explained to match students’ understanding. To score good marks in Class 10 Mathematics examination, it is advised they solve questions provided at the end of each chapter in the ML Aggarwal textbooks for Class 10. This chapter deals with matrices, types of matrices and product of matrices. A rectangular array of m x n numbers (real or complex) in the form of m horizontal lines (called rows) and n vertical lines (called columns), is called a matrix of order m by n, written as m x n matrix. Such an array is enclosed by [ ] or ( ). This chapter of ML Aggarwal Solutions for Class 10 contains three exercises with chapter test. These solutions provided by BYJU’S cover all these concepts, with detailed explanations.

ML Aggarwal Solutions for Class 10 Maths Matrices:-Click Here to Download PDF

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Access answers to ML Aggarwal Solutions for Class 10 Maths Chapter 8 – Matrices

Exercise 8.1

1. Classify the following matrices:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 1

Solution:

It is square matrix of order 2

ML aggarwal Solutions for Class 10 Chapter 8 - Image 2

Solution:

It is row matrix of order 1 × 3

ML aggarwal Solutions for Class 10 Chapter 8 - Image 3

Solution:

It is column matrix of order 3 × 1

ML aggarwal Solutions for Class 10 Chapter 8 - Image 4

Solution:

It is a matrix of order 3 × 2

ML aggarwal Solutions for Class 10 Chapter 8 - Image 5

Solution:

It is a matrix of order 2 × 3

ML aggarwal Solutions for Class 10 Chapter 8 - Image 6

Solution:

It is zero matrix of order 2 × 3

2. (i) If a matrix has 4 elements, what are the possible order it can have?

Solution:

It can have 1 × 4, 4 × 1 or 2 × 2 order.

(ii) If a matrix has 4 elements, what are the possible orders it can have?

Solution:

It can have 1 × 8, 8 × 1, 2 × 4 or 4 × 2 order.

3. Construct a 2 × 2 matrix whose elements aij are given by

(i) aij = 2i – j

(ii) aij =i.j

Solution:

(i) Given aij = 2i – j

Therefore matrix of order 2 × 2 is

ML aggarwal Solutions for Class 10 Chapter 8 - Image 7

(ii) Given aij =i.j

Therefore matrix of order 2 × 2 is

ML aggarwal Solutions for Class 10 Chapter 8 - Image 8

4. Find the values of x and y if:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 9

Solution:

Given

ML aggarwal Solutions for Class 10 Chapter 8 - Image 10

Now by comparing the corresponding elements,

2x + y = 5 ….. i

3x – 2y = 4 ….ii

Multiply (i) by 2 and (ii) by 1 we get

4x + 2y = 10 and 3x – 2y = 4

By adding we get

7x = 14

x = 14/7

x = 2

Substituting the value of x in (i)

4 + y = 5

y = 5 – 4

y = 1

Hence x = 2 and y = 1

5. Find the value of x if

ML aggarwal Solutions for Class 10 Chapter 8 - Image 11

Solution:

Given

ML aggarwal Solutions for Class 10 Chapter 8 - Image 12

Comparing the corresponding terms of given matrix we get

-y = 2

Therefore y = -2

Again we have

3x + y = 1

3x = 1 – y

Substituting the value of y we get

3x = 1 – (-2)

3x = 1 + 2

3x = 3

x = 3/3

x = 1

Hence x = 1 and y = -2

6. If

ML aggarwal Solutions for Class 10 Chapter 8 - Image 13

Find the values of x and y.

Solution:

Given

ML aggarwal Solutions for Class 10 Chapter 8 - Image 14

Comparing the corresponding terms, we get

x + 3 = 5

x = 5 – 3

x = 2

Again we have

y – 4 = 3

y = 3 + 4

y = 7

Hence x = 2 and y = 7

7. Find the values of x, y and z if

ML aggarwal Solutions for Class 10 Chapter 8 - Image 15

Solution:

Given

ML aggarwal Solutions for Class 10 Chapter 8 - Image 16

Comparing the corresponding elements of given matrix, then we get

x + 2 = -5

x = -5 – 2

x = -7

Also we have 5z = -20

z = -20/5

z = – 4

Again from given matrix we have

y2 + y – 6 = 0

The above equation can be written as

y2 + 3y – 2y – 6 = 0

y (y + 3) – 2 (y + 3) = 0

y + 3 = 0 or y – 2 = 0

y = -3 or y = 2

Hence x = -7, y = -3, 2 and z = -4

8. Find the values of x, y, a and b if

ML aggarwal Solutions for Class 10 Chapter 8 - Image 17

Solution:

Given

ML aggarwal Solutions for Class 10 Chapter 8 - Image 18

Comparing the corresponding elements

x – 2 = 3 and y = 1

x = 2 + 3

x = 5

again we have

a + 2b = 5….. i

3a – b = 1 ……ii

Multiply (i) by 1 and (ii) by 2

a + 2b = 5

6a – 2b = 2

Now by adding above equations we get

7a = 7

a = 7/7

a = 1

Substituting the value of a in (i) we get

1 + 2b = 5

2b = 5 -1

2b = 4

b = 4/2

b = 2

9. Find the values of a, b, c and d if

ML aggarwal Solutions for Class 10 Chapter 8 - Image 19

Solution:

Given

ML aggarwal Solutions for Class 10 Chapter 8 - Image 20

Comparing the corresponding terms, we get

3 = d

d = 3

Also we have

5 + c = -1

c = -1 – 5

c = -6

Also we have,

a + b = 6 and a b = 8

we know that,

(a – b)2 = (a + b)2 – 4 ab

(6)2 – 32 = 36 – 32 = 4 = (± 2)2

a – b = ± 2

If a – b = 2

a + b = 6

Adding the above two equations we get

2a = 4

a = 4/2

a = 2

b = 6 – 4

b = 2

Again we have a – b = -2

And a + b = 6

Adding above equations we get

2a = 4

a = 4/2

a = 2

Also, b = 6 – 2 = 4

a = 2 and b = 4

10. Find the values of x, y, a and b, if

ML aggarwal Solutions for Class 10 Chapter 8 - Image 21

Solution:

Given

ML aggarwal Solutions for Class 10 Chapter 8 - Image 22

Comparing the corresponding terms, we get

3x + 4y = 2….i

x – 2y = 4 …..ii

Multiply (i) by 1 and (ii) by 2

3x + 4y = 2, 2x – 4y = 8

Adding the above equations we get

5x = 10

x = 10/5

x = 2

Substituting the value of x in (i)

we get

6 + 4y = 2

4y = 2 – 6

4y = -4

y = -1

Exercise 8.2

ML aggarwal Solutions for Class 10 Chapter 8 - Image 23

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 24

ML aggarwal Solutions for Class 10 Chapter 8 - Image 25

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 26

ML aggarwal Solutions for Class 10 Chapter 8 - Image 27

ML aggarwal Solutions for Class 10 Chapter 8 - Image 28

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 29

ML aggarwal Solutions for Class 10 Chapter 8 - Image 30

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 31

ML aggarwal Solutions for Class 10 Chapter 8 - Image 32

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 33

ML aggarwal Solutions for Class 10 Chapter 8 - Image 34

Find the matrix X if:

(i) 3A + X = B

(ii) X – 3B = 2A

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 35

ML aggarwal Solutions for Class 10 Chapter 8 - Image 36

ML aggarwal Solutions for Class 10 Chapter 8 - Image 37

7. Solve the matrix equation

ML aggarwal Solutions for Class 10 Chapter 8 - Image 38

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 39

ML aggarwal Solutions for Class 10 Chapter 8 - Image 40

Exercise 8.3

ML aggarwal Solutions for Class 10 Chapter 8 - Image 41

Solution:

Yes, the product is possible because of number of column in A = number of row in B

That is order of matrix is 2 × 1

ML aggarwal Solutions for Class 10 Chapter 8 - Image 42

ML aggarwal Solutions for Class 10 Chapter 8 - Image 43

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 44

ML aggarwal Solutions for Class 10 Chapter 8 - Image 45

ML aggarwal Solutions for Class 10 Chapter 8 - Image 46

Find 2PQ

Solution:

Given

ML aggarwal Solutions for Class 10 Chapter 8 - Image 47

ML aggarwal Solutions for Class 10 Chapter 8 - Image 48

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 49

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ML aggarwal Solutions for Class 10 Chapter 8 - Image 51

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 52

ML aggarwal Solutions for Class 10 Chapter 8 - Image 53

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 54

7. Given matrices:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 55

Find the products of

(i) ABC

(ii) ACB and state whether they are equal.

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 56

Now consider,

ML aggarwal Solutions for Class 10 Chapter 8 - Image 57

ML aggarwal Solutions for Class 10 Chapter 8 - Image 58

ML aggarwal Solutions for Class 10 Chapter 8 - Image 59

Solution:

Given

ML aggarwal Solutions for Class 10 Chapter 8 - Image 60

ML aggarwal Solutions for Class 10 Chapter 8 - Image 61

ML aggarwal Solutions for Class 10 Chapter 8 - Image 62

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 53

ML aggarwal Solutions for Class 10 Chapter 8 - Image 64

ML aggarwal Solutions for Class 10 Chapter 8 - Image 65

Find each of the following and state if they are equal.

(i) CA + B

(ii) A + CB

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 66

ML aggarwal Solutions for Class 10 Chapter 8 - Image 67

We can say that CA + B ≠ A + CB

Chapter test

ML aggarwal Solutions for Class 10 Chapter 8 - Image 68

Solution:

Given

ML aggarwal Solutions for Class 10 Chapter 8 - Image 69

comparing the corresponding elements

a + 3 = 2a + 1

⇒ 2a – a =3 – 1

⇒ a = 2 b² + 2 = 3b

⇒ b² – 3b + 2 = 0

⇒ b² – b – 2b + 2 = 0

⇒ b (b – 1) – 2 (b – 1) = 0

⇒ (b – 1) (b – 2) = 0.

Either b – 1 = 0,

then b = 1 or b – 2 = 0,

then b = 2

Hence a = 2, b = 2 or 1

ML aggarwal Solutions for Class 10 Chapter 8 - Image 70

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 71

Now comparing the corresponding elements

3a = 4 + a

a – a = 4

2a = 4

Therefore, a = 2

3b = a + b + 6

3b – b = 2 + 6

2b = 8

Therefore, b = 4

3d = 3 + 2d

3d – 2d = 3

Therefore, d = 3

3c = c + d – 1

3c – c = 3 – 1

2c = 2

Therefore, c = 1

Hence a = 2,b = 4, c = 1 and d= 3

ML aggarwal Solutions for Class 10 Chapter 8 - Image 72

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 73

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