NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1 Matrices - PDF Download

NCERT solutions for class 12 maths chapter 3 exercise 3.1 Matrices stand in for the elements of matrices, order of a matrix, types of matrices and the equality of matrices. This exercise includes questions about building a new matrix for a given element, identifying the orders of a matrix, etc. Through practicing the questions in this exercise, students will gain a good understanding of the concepts of different kinds of matrices and how they are used. 

To comprehend the equality of matrices requires an understanding of the foundations of scalar, diagonal, column, square, and row matrices. Class 12 maths chapter 3 exercise 3.1 NCERT solutions has a total of 10 questions based on the topics and concepts mentioned above. Ex 3.1 class 12 maths solutions are created by the academic mathematics team of mathematics of eSaral to help you with your exam preparation. These solutions are also made available here in PDF format to help you score good marks in final exams. You can download the free PDF of NCERT solutions for ex 3.1 class 12 maths chapter 3 from the official website of eSaral. 

Topics Covered in Exercise 3.1 Class 12 Mathematics Questions

Ex 3.1 class 12 maths ch 3 is described with essential topics such as order of a matrix, types of matrices and equality of matrices. You will be learning these topics here which are elaborated by expert teachers of eSaral.

1. 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. We denote matrices by capital letters.

The numbers or functions are referred to as the terms "elements" or "entries" of the matrix. 

For example - A = $\left[\begin{array}{ll}x & y \\ 1 & 2\end{array}\right]$  

The horizontal lines of elements in above example are referred to as the rows of matrix, and the vertical lines of elements are referred to as its columns.

• Order of a matrix 

It provides information about the number of rows and columns in 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).

(I) We shall follow the notation, namely A = [a_ij]_{m × n} to indicate that A is a matrix of order m × n.

(II) We shall consider only those matrices whose elements are real numbers or functions taking real values.

2. Types of Matrices - Here, we will discuss different types of matrices.

(i) Column matrix - A matrix is said to be a column matrix if it has only one column.

(ii) Row matrix - A matrix is said to be a row matrix if it has only one row.

(iii) Square matrix - A matrix in which the number of rows are equal to the number of columns, is said to be a square matrix. Thus an m × n matrix is said to be a square matrix if m = n and is known as a square matrix of order ‘n’.

(iv) Diagonal matrix - A square matrix B = [b_ij]_{m × m} is said to be a diagonal matrix if all its non diagonal elements are zero, that is a matrix B = [b_ij]_{m × m} is said to be a diagonal matrix if b_ij = 0, when i ≠ j. 

(v) Scalar matrix - A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal, that is, a square matrix B = [b_ij] n × n is said to be a scalar matrix if 

       b_ij = 0, when i ≠ j

       b_ij = k, when i = j, for some constant k.

(vi) Identity matrix - A square matrix in which elements in the diagonal are all 1 and the rest are all zero is called an identity matrix. In other words, the square matrix A = [a_ij]_{n × n} is an identity matrix, if    

   a_ij = $\begin{cases}1 & \text { if } \quad i=j \\ 0 & \text { if } \quad i \neq j\end{cases}$

We denote the identity matrix of order n by I_n . When order is clear from the context, we simply write it as I. 

Observe that a scalar matrix is an identity matrix when k = 1. But every identity matrix is clearly a scalar matrix.

(vii) Zero matrix - A matrix is said to be zero matrix or null matrix if all its elements are zero. Zero matrix is denoted by ‘O’.

• Equality of matrices - Two matrices A = [a_ij] and B = [b_ij] 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 a_ij = b_ij for all i and j

Tips for Solving Exercise 3.1 Class 12 Chapter 3 Matrices

Ex 3.1 class 12 maths chapter 3 has questions which are based on types of matrices, equality of matrix. You can solve these questions by understanding the concepts of matrices. For which our expert faculties of mathematics have provided useful tips to comprehend the concepts and solve the exercise questions.

1. Our subject experts have recommended to follow the illustrative structure of these NCERT solutions for class 12 maths chapter 3 ex 3.1 since it can effectively develop a thorough understanding of difficult subjects over time.

2. With detailed solutions of topics will enable you to solve each question easily.

3. Students must understand the different types of matrices and also practice the examples related to these matrices to solve exercise questions.
   

Importance of Solving Ex 3.1 Class 12 Maths Chapter 3 Matrices

Ex 3.1 class 12 maths ch 3 has questions based on matrices and their applications. By solving these questions, you will get numerous benefits. Some of them are mentioned below.

1. NCERT solutions class 12 maths chapter 3 ex 3.1 describes matrices, their types, order of a matrix in a detailed way so that you can comprehend the conceptual knowledge of these topics to solve exercise 3.1 questions.

2. By solving more questions in NCERT solutions will help you to clear your doubt and build a strong foundation of matrices.

3. Practicing questions from NCERT solutions PDF of class 12 maths chapter 3 ex 3.1 will not only provide you accurate answers but you will be able to cross check your answers.

4. If you revise solving questions again and again in NCERT solutions ex 3.1 will improve your time management skills. 

Frequently Asked Questions

Question 1. What is a matrix?

Answer 1. A matrix is an ordered rectangular array of numbers or functions.

Question 2. What is a row matrix?

Answer 2. A matrix is said to be a row matrix if it has only one row.

Question 3. What is a diagonal matrix?

Answer 3. If all the non diagonal elements of a matrix are zero it is said to be a diagonal matrix.

Question 4. What is an identity matrix?

Answer 4. A square matrix in which elements in the diagonal are all 1 and the rest are all zero is called an identity matrix.