# NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1

NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1 Matrices in Hindi Medium as well as English Medium. In UP Board (Uttar Pradesh Maadhyamik Shiksha Parishad) (Intermediate students), are now using NCERT Books for session 2020-2021. So, these solutions are important not only for CBSE Board but UP Board, MP Board and board also who are following the latest NCERT Textbooks based on latest CBSE Curriculum 2020-2021. Download (Exercise 3.1) here in PDF format to use it offline. 12th Maths Chapter 3 Solutions are available in PDF, Online as well as Video format.

For the online use contents are given below along with the videos format of solutions. These textbook solutions are applicable for UP Board, MP Board, Gujrat board and all other boards who are using NCERT Textbooks as a course book. For any inconvenience, please call or inform us. We will try to help at our level best.## NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1

Class: 12 | Mathematics |

Chapter 3: | Exercise 3.1 Solutions |

### 12th Maths Exercise 3.1 Solutions

NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1 Matrices solutions in English & Hindi Medium are given below updated for new academic session 2020-21. You can download these solutions form the link given at the page. Get here all the exercises of Class 12 Mathematics Chapter 3 main page. Join the discussion forum to share your knowledge with the others in NIOS or CBSE Board concern.

### 12th Maths Exercise 3.1 Solutions in Hindi & English

#### Class 12 Maths Exercise 3.1 Question 1, 2, 3, 4, 5 in Video

#### Class 12 Maths Exercise 3.1 Question 6, 7, 8, 9, 10 in Video

#### Class 12 Maths Exercise 3.1 Question 1, 2, 3, 4 in Hindi Medium

#### Class 12 Maths Exercise 3.1 Question 5, 6 in Hindi Medium

#### Class 12 Maths Exercise 3.1 Question 7, 8, 9, 10 in Hindi Medium

#### Important Terms About Matrices

1. All main diagonal elements of a skew-symmetric matrix are zero.

2. Every square matrix can be uniquely expressed as the sum of a symmetric and a skew symmetric matrix.

3. All positive integral power of a symmetric are symmetric.

4. All odd positive integral power of a skew symmetric matrix are skew symmetric.

##### PROPERTIES OF MATRIX ADDITION

1. Commutativity: If A and B are two matrices of same order, then A + B = B + A.

2. Associativity: If A, B, C are three matrices of same order, then (A + B) + C = A + (B + C).

3. Existence of Identity: The null matrix is the identity element for matrix addition. A + O = O + A = A.

4. Existence of inverse: For every matrix A = [aij, there exists a matrix – A= [-aij] such that A + (-A) = O = (-A) + A.

5. Cancellation laws: If A, B, C are three matrices of the same order, then A + B = A + C implies that B = C and B + A = C + A implies that B = C.

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##### What is a Matrix?

A matrix is an ordered rectangular array of numbers or functions. The numbers or functions are called the elements or the entries of the matrix.

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

A matrix having m rows and n columns is called a matrix of order m × n or simply m × n

matrix (read as an m by n matrix).

##### If a matrix has 8 elements, what are the possible orders it can have?

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

Thus, to find all possible orders of a matrix with 8 elements, we will find all ordered pairs of natural numbers, whose product is 8.

Thus, all possible ordered pairs are (1, 8), (8, 1), (4, 2), (2, 4)

Hence, possible orders are 1 × 8, 8 ×1, 4 × 2, 2 × 4

##### What is a column Matrix?

A matrix is said to be a column matrix if it has only one column.