# NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3

Get the latest and updated NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 (Ex. 3.3) Matrices in Hindi Medium as well as English Medium. Class 12 Maths Solutions are based on the Latest CBSE Curriculum 2021-22 for UP Board and CBSE board Students free to download. You can download 12th Maths Exercise 3.3 in PDF format or go for study online given below. The videos related to all questions of Class 12 Maths Exercise 3.3 are given below along with the PDF solutions. UP Board Solutions for Class 12 Maths Exercise 3.3 is same as CBSE NCERT Solutions of 12th Maths. UP Board Students are now using NCERT Textbooks for Class 12 Maths, so these sols are suitable for him also.

We are working to provide all the content to students free of cost. No login or password is required to access the contents on this website. All the board’s like CBSE, UP Board, MP Board, Gujrat, Uttarakhand and other boards can use these contents if they are following the study material confined to NCERT Books 2021-2022.## NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3

### 12th Maths Exercise 3.3 Solutions in Hindi & English

Class: 12 | Maths (English and Hindi Medium) |

Chapter 3: | Exercise 3.3 |

### 12th Maths Exercise 3.3 Solutions

NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 Matrices in English as well as Hindi Medium are given here to download in PDF format updated for new academic session 2021-2022. UP Board Solutions for 12th Maths for download is also given to use these CBSE NCERT Solutions offline. Get all the exercises of Class 12 Mathematics Chapter 3 from the main page. Download NCERT Books and other textbooks confined to latest CBSE Syllabus and NIOS boards.

#### Class 12 Maths Exercise 3.3 Question 1, 2 and 3 in Video

#### Class 12 Maths Exercise 3.3 Question 4, 5, 6 and 7 in Video

#### Class 12 Maths Exercise 3.3 Question 8, 9 and 10 (I), (II) in Video

#### Class 12 Maths Exercise 3.3 Question 10 (III), IV), 11, 12 in Video

#### Class 12 Maths Exercise 3.3 Question 1, 2, 3 Videos in Hindi

#### Class 12 Maths Exercise 3.3 Question 4, 5 Videos in Hindi

#### Class 12 Maths Exercise 3.3 Question 6, 7 Videos in Hindi

#### Class 12 Maths Exercise 3.3 Question 8, 9, 10 Videos in Hindi

#### Class 12 Maths Exercise 3.3 Question 10, 11, 12 Videos in Hindi

#### 12 Maths Chapter 3 Questions on Matrices with Answers

1. In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.

2. Using determinants, find the equation of line passing through (0, 3) and (1, 1). [Answer: 2x + y = 3]

3. If A be any square matrix of order 3 × 3 and |A| = 5, then find the value of |adj(adjA)|. [Answer: 625]

##### 12th Maths Questions From Board Papers

1. There are two families A and B. There are 4 men, 6 women and 2 children in family A and 2 men, 2 women and 4 children in family B. The recommended daily allowance for calories is Man: 2400, woman: 1900, child: 1800 and for proteins is Man: 55 gm, woman: 45 gm and child: 33 gm. Represent the above information by matrices. Using matrix multiplication, calculate the total requirement of calories and proteins for each of the two families.

2. What is the number of all possible matrices of order 2 × 3 with each entry 0, 1 or 2. [Answer: 729]

3. Given a square matrix A of order 2 × 3 such that |A| = 12, find the value of |A.adjA|. [Answer: 1728]

### Important Questions of 12th Maths Exercise 3.3

##### What do you know about the Equality of matrices?

Two matrices A = [aij] and B = [bij] are said to be equal if

(i) they are of the same order

(ii) each element of A is equal to the corresponding element of B, that is aij = bij for all i and j.

##### What is meant by additive identity?

Let A = [aij] be an m × n matrix and O be an m × n zero matrix, then A + O = O + A = A. In other words, O is the additive identity for matrix addition.

##### What is multiplicative identity of a Matrix?

For every square matrix A, there exist an identity matrix of same order such that IA = AI = A. I is multiplicative identity of the Matrix.

##### What do you understand by transpose of a Matrix?

If A = [aij] be an m × n matrix, then the matrix obtained by interchanging the rows and columns of A is called the transpose of A.

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##### What are the main objectives of exercise 3.3 of 12th Maths?

The main objectives of exercise 3.3 of class 12th Maths are to teach students the following topics:

- Transpose of a matrix
- Properties of the transpose of the matrices
- Symmetric matrices
- Skew symmetric matrices

##### On which theorems questions of exercise 3.3 of 12th Maths are based?

Some questions of exercise 3.3 of class 12th Maths are based on two theorems (theorem 1 and theorem 2) mentioned under section 3.6 of chapter 3 (class 12th Maths).

Theorem 1: For any square matrix A with real number entries, A + A′ is a symmetric matrix and A – A′ is a skew symmetric matrix.

Theorem 2: Any square matrix can be expressed as the sum of a symmetric and a skew symmetric matrix.

##### Is exercise 3.3 of class 12th Maths easy to solve?

Exercise 3.3 (chapter 3 Matrices) of class 12th Maths is the easiest exercise. All questions and examples of this exercise are straightforward. Students enjoy doing this exercise. But difficulty level of any topic/question varies from student to student. So, Exercise 3.3 (chapter 3 Matrices) of class 12th Maths is easy or not depends on students also. Some students find it difficult, and some find it easy.

##### How much time, students need to complete exercise 3.3 of 12th mathematics?

Students need a maximum of 2 days to complete exercise 3.3 (chapter 3) of class 12th mathematics if they give 2 hours per day to this exercise. This time also depends on student’s working speed, efficiency, capability and many other factors.