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

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

3. Simplify:

ML aggarwal Solutions for Class 10 Chapter 8 - 1

Solution:

Given,

ML aggarwal Solutions for Class 10 Chapter 8 - 2

4.

ML aggarwal Solutions for Class 10 Chapter 8 - Image 32

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 33

5. 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

6. 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

7.ML aggarwal Solutions for Class 10 Chapter 8 - 3

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 4

8. ML Aggarwal Solutions for Class 10 Chapter 8 - 5

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 6

9. ML Aggarwal Solutions for Class 10 Chapter 8 - 7

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 8

ML Aggarwal Solutions for Class 10 Chapter 8 - 9

10. ML Aggarwal Solutions for Class 10 Chapter 8 - 10

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 11

On comparing the corresponding elements, we have

8 + y = 0

Then, y = -8

And, 2x + 1 = 5

2x = 5 – 1 = 4

x = 4/2 = 2

Therefore, x = 2 and y = -8

11. ML Aggarwal Solutions for Class 10 Chapter 8 - 12

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 13

On comparing the corresponding terms, we have

2x + 1 = 5

2x = 5 -1 = 4

x = 4/2 = 2

And,

8 + y = 0

y = -8

And, z = 7

Therefore, x = 2, y = -8 and z = 7.

12. ML Aggarwal Solutions for Class 10 Chapter 8 - 14

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 15

Now, comparing the corresponding terms, we get

4 – 4x = -8

4 + 8 = 4x

12 = 4x

x = 12/4

x = 3

And, y + 5 = 2

y = 2 – 5 =

y = -3

Therefore, x = 3 and y = -3

13. ML Aggarwal Solutions for Class 10 Chapter 8 - 16

Find the value of a, b and c.

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 17

Next, on comparing the corresponding terms, we have

a + 1 = 5 ⇒ a = 4

b + 2 = 0 ⇒ b = -2

-c = 3 ⇒ c = -3

Therefore, the value of a, b and c are 4, -2 and -3 respectively.

14. ML Aggarwal Solutions for Class 10 Chapter 8 - 18and 5A + 2B = C, find the values of a, b and c.

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 19

On comparing the corresponding terms, we get

5a + 6 = 9

5a = 9 – 6

5a = 3

a = 3/5

And,

25 + 2b = -11

2b = -11 – 25

2b = -36

b = -36/2

b = -18

And, c = 6

Therefore, the value of a, b and c are 3/5, -18 and 6 respectively.

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 51

3.

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 52

ML aggarwal Solutions for Class 10 Chapter 8 - Image 53

4.

Solution:

ML aggarwal Solutions for Class 10 Chapter 8 - Image 54

5. 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

6.

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

7.

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 - 19

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 20

ML Aggarwal Solutions for Class 10 Chapter 8 - 21

(i) A(B + C) (ii) (B + C)A

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 22

ML Aggarwal Solutions for Class 10 Chapter 8 - 23

10.

Find the matrix C(B – A).

Solution:

Given,

ML Aggarwal Solutions for Class 10 Chapter 8 - 24

ML Aggarwal Solutions for Class 10 Chapter 8 - 25

Find A2 + AB + B2.

Solution:

Given,

ML Aggarwal Solutions for Class 10 Chapter 8 - 26

ML Aggarwal Solutions for Class 10 Chapter 8 - 27

ML Aggarwal Solutions for Class 10 Chapter 8 - 28

12. , find A2 + AC – 5B.

Solution:

Given,

ML Aggarwal Solutions for Class 10 Chapter 8 - 29

ML Aggarwal Solutions for Class 10 Chapter 8 - 30

13. If , find AC + B2 – 10C.

Solution:

Given,

ML Aggarwal Solutions for Class 10 Chapter 8 - 31

ML Aggarwal Solutions for Class 10 Chapter 8 - 32

ML Aggarwal Solutions for Class 10 Chapter 8 - 33

14. If find A2 and A3. Also state that which of these is equal to A.

Solution:

Given,

ML Aggarwal Solutions for Class 10 Chapter 8 - 34

From above, its clearly seen that A3 = A.

ML Aggarwal Solutions for Class 10 Chapter 8 - 35

15. If show that 6X – X2 = 9I where I is the unit matrix.

Solution:

Given,

ML Aggarwal Solutions for Class 10 Chapter 8 - 36

– Hence proved

ML Aggarwal Solutions for Class 10 Chapter 8 - 37

16. Show that is a solution of the matrix equation X2 – 2X – 3I = 0, where I is

the unit matrix of order 2.

Solution:

Given,

ML Aggarwal Solutions for Class 10 Chapter 8 - 38

17. Find the matrix 2 × 2 which satisfies the equation

ML Aggarwal Solutions for Class 10 Chapter 8 - 39

Solution:

Given,

ML Aggarwal Solutions for Class 10 Chapter 8 - 40

ML Aggarwal Solutions for Class 10 Chapter 8 - 41

18. If find the value of x, so that A2 – 0

Solution:

Given,

ML Aggarwal Solutions for Class 10 Chapter 8 - 42

On comparing,

1 + x = 0

∴ x = -1

19.

ML Aggarwal Solutions for Class 10 Chapter 8 - 43

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 44

Comparing the corresponding elements,

– 3x + 4 = -5

-3x = -5 – 4 = -9

x = -9/-3 = 3

Therefore, x = 3 and y = -10.

ML Aggarwal Solutions for Class 10 Chapter 8 - 45

Comparing, we get

8x = 16

⇒ x = 16/8 = 2

And, 9y = 9

y = 9/9 = 1

ML Aggarwal Solutions for Class 10 Chapter 8 - 46

20. Find the values of x and y if

Solution:

Given,

ML Aggarwal Solutions for Class 10 Chapter 8 - 47

On comparing the corresponding elements, we have

2x + y = 3 … (i)

3x + y = 2 … (ii)

Subtracting, we get

-x = 1 ⇒ x = -1

Substituting the value of x in (i),

2(-1) + y = 3

-2 + y = 3

y = 3 + 2 = 5

Therefore, x = -1 and y = 5.

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

3. Determine the matrices A and B when

ML Aggarwal Solutions for Class 10 Chapter 8 - 48

Solution:

Given,

ML Aggarwal Solutions for Class 10 Chapter 8 - 49

4.

ML Aggarwal Solutions for Class 10 Chapter 8 - 50

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 51

Comparing the corresponding elements, we have

4 + 2a = 18

2a = 18 – 4 = 14

a = 14/2

⇒ a = 7

1 + 2b = 7

2b = 7 – 1 = 6

b = 6/2

⇒ b = 3

2 + 2c = 14

2c = 14 – 2 = 12

2c = 12

c = 12/2

⇒ c = 6

3 + 2d = 11

2d = 11 – 3

d = 8/2

⇒ d = 4

Therefore, a = 7, b = 3, c = 6 and d = 4.

ML Aggarwal Solutions for Class 10 Chapter 8 - 52

ML Aggarwal Solutions for Class 10 Chapter 8 - 53

ML Aggarwal Solutions for Class 10 Chapter 8 - 54

5. If , find the each of the following and state it they

are equal:

(i) (A + B) (A – B)

(ii) A2 – B2

Solution:

Given,

ML Aggarwal Solutions for Class 10 Chapter 8 - 55

ML Aggarwal Solutions for Class 10 Chapter 8 - 56
Hence, its clearly seen that (A + B) (A – B) ≠ A2 – B2.

ML Aggarwal Solutions for Class 10 Chapter 8 - 57

6. If , find A2 – 5A – 14I, where I is unit matrix of order 2 × 2.

Solution:

Given,

ML Aggarwal Solutions for Class 10 Chapter 8 - 58

ML Aggarwal Solutions for Class 10 Chapter 8 - 59

ML Aggarwal Solutions for Class 10 Chapter 8 - 60

7. If and A2 = 0, find p and q.

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 61

On comparing the corresponding elements, we have

9 + 3p = 0

3p = -9

p = -9/3

p = -3

And,

9 + 3q = 0

3q = -9

q = -9/3

q = -3

Therefore, p = -3 and q = -3.

ML Aggarwal Solutions for Class 10 Chapter 8 - 62

8. If find a, b, c and d.

Solution:

Given,

ML Aggarwal Solutions for Class 10 Chapter 8 - 63

On comparing the corresponding elements, we have

-a = 1 ⇒ a = -1

-b = 0 ⇒ b = 0

c = 0 and d = -1

Therefore, a = -1, b = 0, c = 0 and = -1.

ML Aggarwal Solutions for Class 10 Chapter 8 - 64

9. Find a and b if

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 65

On comparing the corresponding terms, we have

2a – 4 = 0

2a = 4

a = 4/2

a = 2

And, 2a – 2b = -2

2(2) – 2b = -2

4 – 2b = -2

2b = 4 + 2

b = 6/2

b = 3

Therefore, a = 2 and b = 3.

ML Aggarwal Solutions for Class 10 Chapter 8 - 66

10. If

Find (i) 2A – 3B (ii) A2 (iii) BA

Solution:

ML Aggarwal Solutions for Class 10 Chapter 8 - 67

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