** ** **NCERT Solutions for Maths Class 12 Exercise 3.1**

Hello Students! Welcome to **maths-formula.com**. In this post, you will find the complete** ****NCERT Solutions for Maths Class 12 Exercise 3.1**.

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Class 12th is a very crucial stage of your student’s life, since you take all important decisions about your career on this stage. Mathematics plays a vital role to take decision for your career because if you are good in mathematics, you can choose engineering and technology field as your career.

**NCERT Solutions for Maths Class 12 Exercise 3.1** helps you to solve each and every problem with step by step explanation which makes you strong in mathematics.

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**NCERT Solutions for Maths Class 12 Exercise 3.1** are prepared by the experienced teachers of CBSE board. If you are preparing for JEE Mains and NEET level exams, then it will definitely make your foundation strong.

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**NCERT Solutions for Maths Class 12 Exercise 3.2**

**NCERT Solutions for Maths Class 12 Exercise 3.3**

**NCERT Solutions for Maths Class 12 Exercise 3.4**

**NCERT Solutions for Maths Class 12 Exercise 3.1**

**Maths Class 12 Ex
3.1 Question 1.**

**In the
matrix **

**Write:**

**(i) The order of the matrix,**

**(ii) The number of elements,**

**(iii) Write the elements a _{13}, a_{21}, a_{33}, a_{24},
a_{23}. **

**Solution:**

**(i)** The matrix A has 3 rows and 4
columns.

Therefore, the order of the matrix is 3 × 4.

**(ii)** There are 3 × 4 = 12 elements
in the matrix A.

**(iii)** In the given matrix, a_{13} =
19, a_{21} = 35, a_{33} = – 5, a_{24} =
12, a_{23} = 5/2

**Maths Class 12 Ex
3.1 Question 2.**

**If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?**

**Solution:**

We know that if a matrix is of order m × n, then it has mn elements.

**(i)** We have, 24 = 1 × 24 = 2 × 12 =
3 × 8 = 4 × 6

Thus, there are 8 matrices having 24 elements and their orders are (1 × 24),
(24 × 1), (2 × 12), (12 × 2), (3 × 8), (8 × 3), (4 × 6), (6 × 4).

**(ii)** We have, 13 = 1 × 13,

Thus, there are 2 matrices of 13 elements and their orders are (1 × 13) and (13
× 1).

**Maths Class 12 Ex
3.1 Question 3.**

**If a matrix has 18 elements, what are the possible orders it can have ? What, if it has 5 elements.**

**Solution:**

We know that if a matrix is of order m × n, then it has mn elements.

**(i)** We have, 18 = 1 × 18 = 2 × 9 = 3
× 6

Thus, there are 6 matrices having 18 elements and their orders are (1 × 18), (18
× 1), (2 × 9), (9 × 2), (3 × 6), (6 × 3).

**(ii)** We have, 5 = 1 × 5

Thus, there are 2 matrices of 5 elements and their orders are (1 × 5) and (5 ×
1).

**Maths Class 12 Ex
3.1 Question 4.**

**Construct a 2**

**× 2 matrix, A = [**

*a*], whose elements are given by:_{ij}**Solution:**

**Maths Class 12 Ex
3.1 Question 5.**

**Construct a 3**

**× 4 matrix, whose elements are given by:**

**Solution:**

**Maths Class 12 Ex
3.1 Question 6.**

**Find the values of x, y and z from the following equations:**

**Solution:**

x² – 6x + 8 = 0

(x – 4)(x – 2) = 0

Therefore, x = 2, 4

When x = 2, y = 6 – 2 = 4 and when x = 4, y = 6 – 4 = 2

Hence, x = 2, y = 4, z = 0 or x = 4, y = 2, z = 0.

(iii) Equating
the corresponding elements, we get

x + y + z = 9 …..(i)

x + z = 5 ..…(ii)

y + z = 7 ..…(iii)

Adding equations (ii) and (iii), we get

x + y + 2z = 12

(x + y + z) + z = 12

9 + z = 12 [From equation (i)]

z = 3

x + z = 5

x + 3 = 5

Therefore, x = 2

From equation
(iii), y + z = 7

y + 3 = 7

y = 4

Hence, x = 2, y = 4 and z = 3.

**Maths Class 12 Ex
3.1 Question 7.**

**Find the values of a,b,c and d from the equation:**

**Solution:**

Equating the elements of both the matrices.

**Maths Class 12 Ex
3.1 Question 8.**

**A = [a _{ij}]_{m × n} is a square matrix, if**

**(A) m < n (B) m > n (C) m = n (D) None of these**

**Solution:**

For a square matrix, m = n.

Hence, option (C) is correct.

**Maths Class 12 Ex
3.1 Question 9.**

**Which of the given values of x and y make the following pairs of matrices equal:**

**(A) x = –1/3, y = 7**

**(B) Not possible to find**

**(C) y = 7, x = –2/3**

**(D) x = –1/3, y = –2/3**

**(a)** x = –1/3, y = 7

**Maths Class 12 Ex
3.1 Question 10.**

**The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is**

**(A) 27**

**(B) 18**

**(C) 81**

**(D) 512**

**Solution:**

The matrix is of order 3 × 3, therefore,
there are 9 entries in the matrix, each place can be filled with 0 or 1.

Then, 9 places can be filled in 2^{9} =
512 ways

Thus, the number of such matrices = 512

Hence, option (D) is correct.

**NCERT Solutions for Maths Class 12 Exercise 3.2**