NCERT Solutions for Class 9 Political Science Chapter 2

August 8, 202239 Insightful Publications

**Exercise 3.1 Class 12 Maths NCERT Solutions: **The CBSE Class 12 board exams started on April 26, 2022, and the date for the Maths exam was June 7, 2022. Students have to be thorough with the NCERT books and solutions to score well in the CBSE Class 12 exam. This article deals with the Class 12 Maths Chapter 3 Exercise 3.1, Matrices and the following chapter Determinants, which carries a weightage of 10 marks.

Embibe provides Exercise 3.1 Class 12 Maths NCERT Solutions in this article for students to practice for free. Students must keep in mind that NCERT in-text questions should be the first priority while they prepare for the CBSE Class 12 board exam. The solutions provided here at Embibe are designed by experts and students can rely on them. Read through the article to find out more about the subject overview, the benefits of solving the NCERT questions, and much more!

Here we have provided an overview of the chapter for students to understand the chapter thoroughly before they start practicing for the CBSE Class 12 board exam:

Class | Class 12 |

Chapter Name | Matrix |

Exercise Number | Ex 3.1 |

Topic Name | Introduction to Matrices |

Language | English |

Solution Type | In-text Solved Questions |

Official Website | https://ncert.nic.in/ |

Here we have provided the NCERT Solutions for Class 12 Maths Exercise 3.1 questions along with the answers in the link below for students to refer to. Students can bookmark the page and use it for future reference as well.

**Practice Chapter 3 Class 12 Exercises For Free!**

**Free PDF Links of Chapter 12 Exercises**

Please find the PDF links for the exercises below, including the Chapter 3 Ex 3.1 solutions:

Chapter 3 Class 12 Exercise 3.1 Free PDF | Chapter 3 Class 12 Exercise 3.3 Free PDF |

Chapter 3 Class 12 Exercise 3.2 Free PDF | Chapter 3 Class 12 Exercise 3.4 Free PDF |

**Question: **Construct a 3×4 matrix, whose elements are given by

aij=12|-3i+j|**Solution: **To construct: A 3×4 matrix. It has 3 rows and 4 columns

Let the required matrix be A.

Where A=a11a12a13a14a21a22a23a24a31a32a33a343×4

It is given that aij=12|-3i+j|

aij i=, j= aij=12|-3i+j|

a11 i=1, j=1 a11=12|-3(1)+1|=12|-3+1|=12|-2|=12(2)=1

a12 i=1, j=2 a12=12|-3(1)+2|=12|-3+2|=12|-1|=12(1)=12

a13 i=1, j=3 a13=12|-3(1)+3|=12|0|=12(0)=0

a14 i=1, j=4 a14=12|-3(1)+4|=12|-3+4|=12|1|=12(1)=12

a21 i=2, j=1 a21=12|-3×2+1|=12|-6+1|=12|-5|=12(5)=52

a22 i=2, j=2 a22=12|-3×2+2|=12|-6+2|=12|-4|=12(4)=2

a23 i=2, j=3 a23=12|-3(2)+1|=12|-6+3|=12|-3|=12(3)=32

a24 i=2, j=4 a24=12|-3×2+2|=12|-6+4|=12|-2|=12(2)=1

a31 i=3, j=1 a31=12|-3(3)+1|=12|-9+1|=12|-8|=12(8)=4

a32 i=3, j=2 a32=12|-3(3)+2|=12|-9+2|=12|-7|=12(7)=72

a33 i=3, j=3 a33=12|-3×3+3|=12|-9+3|=12|-6|=12(6)=3

a34 i=3, j=4 a34=12|-3×3+4|=12|-9+4|=12|-5|=12(5)=52

Hence, the required matrix is

A=112012522321472352

**Question: ** Construct a 3×4 matrix, whose elements are given by:

aij=2i-j**Solution: **To construct: A 3×4 matrix it has 3 rows and 4 columns

Let the required matrix be A.

Where A=a11a12a13a14a21a22a23a24a31a32a33a343×4

It is given that

aij=2i-j

Therefore, a11=2(1)-1=2-1=1 a12=2(1)-2=2-2=0 a13=2(1)-3=2-3=-1 a14=2(1)-4=2-4=-2 a21=2(2)-1=4-1=3 a22=2(2)-2=4-2=2 a23=2(2)-3=4-3=1

a24=2(2)-4=4-4=0 a31=2(3)-1=6-1=5 a32=2(3)-2=4 a33=2(3)-3=3 a34=2(3)-4=2

Therefore, the required matrix A=10-1-232105432

Students have to be thorough with Class 12 Maths Chapter 3 Exercise 3.1 in order to proceed to other topic-wise exercises. These are basic questions of matrices as the exercise deals with the introduction to matrices.

By practicing the NCERT Solutions for the exercises, students can score great marks in the CBSE Class 12 board exams. Introduction to Matrices deals with formulas and ideas like:

If A, B are square matrices of order n, and I_{n} is a corresponding unit matrix, then

**(a) **A(adj.A) = | A | I_{n} = (adj A) A

**(b) **| adj A | = | A |n^{-1} (Thus A (adj A) is always a scalar matrix)

**(c) **adj (adj.A) = | A |^{n-2} A, and so on.

**Practice 12th CBSE Exam Questions**

Imagine a rectangular pattern of numbers m times n, be it real or complex numbers, in the array of m horizontal lines (rows) and n vertical lines (columns). This is called the matrix of order m x n. This is marked by [ ] or ( ). It comprises the following topics:

- Introduction to Matrices
- Types of Matrices
- Matrix Operations
- Adjoint and Inverse of a Matrix
- The Rank of a Matrix and Special Matrices
- Solving Linear Equations using Matrix

Students can easily score full marks in the chapter Matrices, only when they understand the concepts well. Most of the long answers type of questions are often asked from this chapter. Students can learn the Matrix concepts from the in-text questions asked and we have provided all the details of Exercise 3.1 Class 12 Maths in this article for the students to begin their practice.

Here we have provided a few important questions from the chapter in general for the students to practice better.

**1 Mark Questions**

Provided below is the list of 1-mark questions:

- If a matrix has 8 elements, what are the possible orders it can have?
- Identity matrix of orders n is denoted by?
- The number of all possible metrics of order 3 3 with each entry 0 or 1 is?
- Two matrices A = aij and B = bij are said to be equal if?
- Every diagonal element of a skew-symmetric matrix is?

**4 Mark Questions**

Provided below is the list of 4-mark questions:

- Show that f(x). f(y) = f(x+y)
- Construct a 3 times 4 matrix, whose elements are given by aij = 1 by 2 of the order negative 3 i added to j.
- Obtain the inverse of the following matrix using elementary operations

A equals [ 0 1 2 ]

[ 1 2 3]

[ 3 1 1]

For the descriptive NCERT solutions and important questions, click here!

There are numerous advantages to solving the NCERT textbook questions. These questions are the standard questions provided by the CBSE board for the students to practice and understand every concept. Here are a few benefits of solving the NCERT in-text questions:

**Clear Comprehension of Topics:**The NCERT step-by-step explanation given for each question is concise and on-point. Hence, students can understand the topics better as they practice these in-text questions along with their solutions. A clear-cut understanding of the topics is necessary to score the highest marks in Maths. It is a subject that demands extensive practice from the students and solving NCERT questions is the best way to better yourselves in Maths.**Management of Time:**When the student practices the NCERT questions which include the short answers and long answers, one can learn the skill of time management. This will help them to solve the questions easily when it comes to board exams. Most of the students complain about the lack of time when it comes to the CBSE Class 12 Maths exam. By solving the NCERT questions, students will get a knack for solving the questions on time.**Types of Questions:**Students often get confused when they see a lot of questions all of a sudden on the board exam papers. But, the NCERT question pattern follows the CBSE curriculum and students will get to practice a variety of questions. From very short answer to long answer questions, the NCERT textbooks have them all.**Best for Competitive Exams:**The NCERT textbooks are the ideal reference books for any JEE, NEET, or competitive exam aspirants. The concepts a student must be thorough with are given in the respective NCERT textbooks. In all the coaching classes for any competitive exam, the first step is to practice the NCERT textbook questions and solutions to grasp the concepts well.

We have provided a few frequently asked questions on the CBSE Class 12 Maths NCERT questions and solutions along with the answers. Students can refer to the solutions to resolve their doubts. Please go through the FAQs given below:

**Q.1. Where can I download the free PDF of all NCERT** **questions and solutions for Maths?****Ans:** Students can download the free PDF of all chapters’ Maths NCERT questions and solutions from Embibe. Embibe provides accurate study materials, mock test series, and NCERT questions along with the solutions, chapter-wise for all subjects. They are completely free and students can easily access them at any time after downloading. Students can also check the official NCERT website for more information on books and solutions.

**Q.2. How important is Exercise 3.1 of Matrices for the Class 12 board exam?Ans: **Matrices is an important chapter in the CBSE Class 12 Maths syllabus. Matrices and Determinants carry a weightage of 10 marks and Exercise 3.1 covers the basic concepts that can be asked for very short answer and short answer questions. Students must be thorough with the basics to move forward and understand the complete chapter. So, Exercise 3.1 is very important for the students to practice.

**Q.3. What are a few important topics covered under Class 12 Matrices? ****Ans: ** Here are a few important topics covered in Chapter 3, Matrices, for Class 12:

- Matrix and operation on matrices
- Types of matrix
- Transpose of a matrix, symmetric, and skew-symmetric matrix
- Conjugate of matrix, hermitian, and skew-hermitian matrix
- Determinant of matrix
- Minor and cofactor of an element of matrix/determinant
- Adjoint and inverse of a matrix
- Elementary row operations and their use in finding the inverse of a matrix
- System of linear equations and Cramer’s rule
- System of homogeneous linear equations

**Q.4. Is the topic Matrix an easy topic to understand?****Ans: **Yes! Matrix is an easy topic to understand compared to other chapters in the CBSE Class 12 Maths syllabus. Students must be familiar with the type of matrices and not make careless mistakes while doing the operations on a matrix. Keep the rows and columns in mind and continue with the operations on matrices. Otherwise, Matrices is an easy chapter.

**Q.5. What is the pass mark for the CBSE Class 12 exam?****Ans: **A student must obtain at least 33% in the CBSE Class 12 Maths exam to pass the exam.

**Attempt 12th CBSE Exam Mock Tests**

**Related Links: **

*With a focused mind and utmost dedication, students can easily tackle the CBSE Maths Class 12 examination. Students can pass with flying colours and score 100/100 with the right guidance. We hope that the article on NCERT Solutions for Matrices Exercise 3.1 Class 12 Maths will help the students resolve their doubts. *

*Stay tuned to Embibe for more such content! Happy learning!*

** **