# 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 file format to use it offline. 12th Maths Chapter 3 Solutions are available in PDF, Online as well as Video format.

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## 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 and 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.

##### 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.

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