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# NCERT Solutions for Class 12 Maths Matrices

Hi Students, Welcome to **Amans Maths Blogs (AMB)**. In this post, you will get the * NCERT Solutions for Class 12 Maths Matrices Exercise 3.1*. This

**can be downloaded in PDF file. The downloading link is given at last.**

*NCERT Solutions** NCERT Solutions for Class 12 Maths* are not only the solutions of Maths exercise but it builds your foundation of other important subjects. Getting knowledge of depth concept of

*like Algebra, Calculus, Trigonometry, Coordinate Geometry help you to understand the concept of Physics and Physical Chemistry.*

**CBSE Class 12**^{th}Maths* CBSE Class 12^{th}* is an important school class in your life as you take some serious decision about your career. And out of all subjects, Maths is an important and core subjects. So

*is major role in your exam preparation as it has detailed chapter wise solutions for all exercise.*

**CBSE NCERT Solutions for Class 12**^{th}MathsAs we know that all the schools affiliated from CBSE follow the NCERT books for all subjects. You can check the **CBSE NCERT Syllabus**. Thus, * NCERT Solutions* helps the students to solve the exercise questions as given in

*.*

**NCERT Books**## NCERT Solutions for Class 12 Maths Matrices Exercise 3.1

**NCERT Solutions for Class 12 Maths Matrices ****Exercise**** 3.1: Ques No 1.**

In the matrix, write.

(a) The order of the matrix

(b) The number of elements

(c)Write the elements a_{13}, a_{21}, a_{33}, a_{24}, a_{23}.

**NCERT Solutions:**

(a) In the given matrix, the number of rows is 3 and the number of columns is 4. Therefore, the order of the matrix is 3 x 4.

(b) The number of elements is 3 x 4 = 12.

(c) a_{13 }= 19, a_{21 }= 35, a_{33 }= -5, a_{24 }= 12, a_{23 }= 5/2.

**NCERT Solutions for Class 12 Maths Matrices ****Exercise**** 3.1: Ques No 2.**

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

**NCERT Solutions:**

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

Thus, to find all the possible orders of a matrix having 24 elements, we have to find all the ordered pairs of natural numbers whose product is 24.

Since 24 = 1 x 24 = 2 x 12 = 3 x 8 = 4 x 6, then the possible order of the matrix is

1 x 24 or 24 x 1; 2 x 12 or 12 x 2; 3 x 8 or 8 x3; 4 x 6 or 6 x 4.

If the matrix has 13 elements, then the possible order of the matrix is 1 x 13 or 13 x 1.

**NCERT Solutions for Class 12 Maths Matrices ****Exercise**** 3.1: Ques No 3.**

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

**NCERT Solutions:**

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

Thus, to find all the possible orders of a matrix having 18 elements, we have to find all the ordered pairs of natural numbers whose product is 18.

Since 18 = 1 x 18 = 2 x 9 = 3 x 6, then the possible order of the matrix is

1 x 18 or 18 x 1; 2 x 9 or 9 x 2; 3 x 6 or 6 x 3;

If the matrix has 5 elements, then the possible order of the matrix is 1 x 5 or 5 x 1.

**NCERT Solutions for Class 12 Maths Matrices ****Exercise**** 3.1: Ques No 4.**

Construct a 2 × 2 matrix, A = [a_{ij}], whose elements are given by (i) a_{ij} = (i + j)^{2}/2

**NCERT Solutions:**

A 2 x 2 matrix has two rows and two columns. Thus, it is denoted by.

Construct a 2 × 2 matrix, A = [a_{ij}], whose elements are given by (ii) a_{ij} = i/j.

**NCERT Solutions:**

A 2 x 2 matrix has two rows and two columns. Thus, it is denoted by.

Construct a 2 × 2 matrix, A = [a_{ij}], whose elements are given by (i) a_{ij} = (i + 2j)^{2}/2

**NCERT Solutions:**

A 2 x 2 matrix has two rows and two columns. Thus, it is denoted by.

**NCERT Solutions for Class 12 Maths Matrices ****Exercise**** 3.1: Ques No 5.**

Construct a 3 × 4 matrix, A = [a_{ij}], whose elements are given by (i) a_{ij} = (1/2)| -3i + j |.

**NCERT Solutions:**

A 3 x 4 matrix has three rows and four columns. Thus, it is denoted by .

Construct a 3 × 4 matrix, A = [a_{ij}], whose elements are given by (ii) a_{ij} = 2i – j.

**NCERT Solutions:**

A 3 x 4 matrix has three rows and four columns. Thus, it is denoted by .

**NCERT Solutions for Class 12 Maths Matrices ****Exercise**** 3.1: Ques No 6.**

Find the values of x, y and z from the following equations: (i).

**NCERT Solutions:**

In equal matrices, the corresponding elements are equal.

Thus, from the given matrices, we get x = 1, y = 4 and z = 3.

Find the values of x, y and z from the following equations: (ii).

**NCERT Solutions:**

In equal matrices, the corresponding elements are equal.

Thus, from the given matrices, we have

x + y = 6 ⟹ y = 6 – x,

xy = 8

and 5 + z = 5 ⟹ z = 0.

Now, put y = 6 – x in xy = 8, then x(6 – x) = 8 ⟹ 6x – x^{2} = 8 ⟹ x^{2} – 6x + 8 = 0 ⟹ (x – 4)(x – 2) = 0 ⟹ x = 2 or 4 ⟹ y = 4 or 2

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

Find the values of x, y and z from the following equations: (iii).

**NCERT Solutions:**

In equal matrices, the corresponding elements are equal.

Thus, from the given matrices, we have

x + y + z = 9

x + z = 5 ⟹ x = 5 – z

and y + z = 7 ⟹ y = 7 – z

Now, put x = 5 – z and y = 7 – z in x + y + z = 9, then

Thus, 5 – z + 7 – z + z = 9 ⟹ z = 3 ⟹ x = 2 and y = 4

Therefore, x = 2, y = 4, z = 3.

**NCERT Solutions for Class 12 Maths Matrices ****Exercise**** 3.1: Ques No 7.**

Find the value of a, b, c and d from the equation: (i).

**NCERT Solutions:**

In equal matrices, the corresponding elements are equal.

Thus, from the given matrices, we have

a – b = -1 ⟹ a = b – 1

2a – b = 0 ⟹ 2(b – 1) – b = 0 ⟹ b = 2 ⟹ a = 1

2a + c = 5 ⟹ 2 + c = 5 ⟹ c = 3

3c + d = 13 ⟹ 9 + d = 13 ⟹ d = 4

Thus, a = 1, b = 2, c = 3 and d = 4.

**NCERT Solutions for Class 12 Maths Matrices ****Exercise**** 3.1: Ques No 8.**

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

(A) m < n, (B) m > n, (c) m = n, (D) None of these

**NCERT Solutions:**

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

**NCERT Solutions for Class 12 Maths Matrices ****Exercise**** 3.1: Ques No 9.**

Which of the given values of x and y make the following pair of matrices equal?

**NCERT Solutions:**

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

**NCERT Solutions for Class 12 Maths Matrices ****Exercise**** 3.1: Ques No 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

**NCERT Solutions:**

The matrix has 3 x 3 = 9 elements with the entries 0 or 1.

Thus, the number of possible matrices is 2^{9} = 512.