NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1 (Ex 3.1)

Mathematics is a conceptual subject that requires a large amount of practice. Students need to have clear and strong basics of the subject to score well in it. Along with being a subject taught in school, Mathematics is also the base for many scientific subjects and theories. Class 12 Mathematics contains a huge number of concepts, so it is difficult for students to have a hold of all the concepts of the curriculum of the subject. The primary key to scoring well in Mathematics is practice. Extramarks provides students with the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 so that they can practice the solutions and have deep understanding of Chapter-3 Matrices. The first step for the students to build strong fundamentals in Mathematics is to practice the NCERT Textbook multiple times. Extramarks provides students with the Class 12 Maths NCERT Solutions Chapter 3 Matrices Exercise 3.1 to learn, prepare and excel in their board examinations.

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Chapter-3 Matrices is not only a part of the Class 12 Mathematics curriculum but is also a concept found in other fields as well. It is one of the most applied concepts in the field of Mathematics and has made the solutions to various problems easier. Matrix is not a straight method of applied Mathematics but has made Mathematical operations a lot more effortless rather than straightforward methods. Therefore, students need to learn about matrices in Class 12 because the students who have opted for Mathematics in Class 12 are looking forward to learning it for further studies. For higher studies in fields like Electrical Circuits, Quantum Physics, Optics etc, matrices are very useful. Matrices also have daily use practical applications. Some of its real-life applications are in Encryption, 3D Games, Economics, etc.

Click on the given link to download the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1.

NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1 (Ex 3.1)

Students can download the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 from the Extramarks’ website. Students can easily find the solutions to the Ex 3.1 Class 12th Maths online, but the solutions must be correct and up to date. The NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 provided by Extramarks are reliable solutions that are properly detailed and explained in a step-by-step approach.

Access NCERT Solutions for Class 12 Maths Chapter 3 – Matrices

Students can easily access the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 on any device as these solutions can be downloaded in PDF format. Extramarks provides students with the easily accessible study material that can be used anytime and anywhere.

Matrices Class 12 NCERT Solutions 3.1 Available

The NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 provided by Extramarks are curated by the subject experts of the organization. The Class 12 Maths Chapter 3 Exercise 3.1 solutions provided by Extramarks are accurate and properly detailed so that the students can have ready access to handy and authentic study material. Extramarks recommends that students download the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 so that they can understand the concepts through the solutions and then practice them thoroughly. This helps the students with a steady pace and a clear understanding of concepts so that they can solve all the difficult problems of Chapter-3 Matrices very precisely and fast.

There is a basic format in which matrices are solved, they are written in rows and columns in a format like this-

⎡ 1 9 -13 ⎤

⎣ 20 5 -6 ⎦

There are two rows and three columns of matrix. It can also be referred to as a two-by-three matrix. Square matrices are the most essential type of matrices and are also the most applied matrices. Square matrices have the same number of rows and columns. The determinant of a square matrix is a number associated with the matrix, which is the base for the study of a square matrix. Some students can find it difficult to understand the concepts and calculations of matrices. The NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 provided by Extramarks makes it easier for students to understand the complicated calculations involved in Chapter 3 Matrices. Extramarks provides students with expert solutions and live problem-solving classes so that students can learn efficiently and score well in their board exams.

NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1.

Chapter 3 Matrix Exercises
Exercise 3.2	22 Questions & Solutions (3 Short Answers, 19 Long Answers)
Exercise 3.3	12 Questions & Solutions (4 Short Answers, 8 Long Answers)
Exercise 3.4	18 Questions & Solutions (18 Short Answers)

Step By Step Solutions For Class 12 Maths Chapter 3 Exercise 3.1

The NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 provided by Extramarks are very useful at the time of quick revisions. But, if the solutions are not explained in proper steps, it becomes challenging for the students to clear their doubts. Also in Mathematics, students can score marks based on step-wise marking. Extramarks provides students with the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 which are step-by-step solutions.

What is there In Class 12th NCERT Maths Chapter 3 Matrices Exercise 3.1?

The NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 are based on the subtopics Introduction, Matrix, Order of a Matrix, Types of Matrices, and Equality of Matrices. The exercise is composed of ten questions based on these topics. Students of Class 12 are required to have the NCERT curriculum on their fingertips. These books are the first step for them to build their fundamentals and clear their basic concepts. Students need to have the solutions to the NCERT questions in hand so that they do not waste their time looking for them. Extramarks provides students with the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 so that they can get authentic solutions without having to look anywhere else.

Chapter 3, Matrices of Class 12 Mathematics, is one of the most scoring chapters in the curriculum of Class 12 Maths. Once students understand the concepts of the chapter, they can solve any questions related to that chapter easily, but for that, they need to thoroughyl practice the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1. Extramarks provides students with complete and ready study material. Since NCERT covers all the syllabus of the curriculum of the subject, students must have access to the NCERT Solutions in all the classes. Extramarks provides students with the NCERT Solutions Class 12, NCERT Solutions Class 11, NCERT Solutions Class 10, NCERT Solutions Class 9, NCERT Solutions Class 8, NCERT Solutions Class 7, NCERT Solutions Class 6, NCERT Solutions Class 5, NCERT Solutions Class 4, NCERT Solutions Class 3, NCERT Solutions Class 2, NCERT Solutions Class 1 and much more so that the students can have access to ready study material.

Important Topics Covered under Class 12th NCERT Maths Chapter 3 Matrices Exercise 3.1

NCERT books are written by subject experts, so if students thoroughly go through the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1, they acknowledge all the concepts. Class 12 Maths Chapter 3 Exercise 3.1 provided by Extramarks makes students ready for their board examinations and maintains their confidence.

Importance of Class 12 Maths Chapter 3 Matrix

Matrices are defined as a set of numbers arranged in rows and columns to form a rectangular array. The numbers are referred to as the Elements, or Entries, of the Matrix. Matrices have wide applications in Engineering, Economics, Statistics, and Physics as well as in various branches of Mathematics. Matrices is a topic that requires a huge amount of practice like any other topic in Mathematics, but its concepts and calculations are a bit different from the rest of the chapters in Mathematics. So for learning and understanding this chapter, Extramarks recommends students to go through the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 thoroughly, so that they can have deeper understanding of the concepts. The NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 provided by the Extramarks’ website gives the students an overview of all the properties of Matrices, followed by giving solved answers to the chapter. By going through these solutions, students can achieve their goals and score well in the board examination.

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Get Solutions For The Complete Matrices Ex- 3.1 At One Place

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Get Access To Extramarks Ex 3.1 Class 12 Maths Solutions Today

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Q.1

\begin{array}{l} In a matrix A = [\begin{array}{l} 2 5 19 - 7 \\ 35 - 2 \frac{5}{2} 12 \\ \sqrt{3} 1 - 5 17 \end{array}], write : \\ (i) The order of the matrix \\ (ii) Then umber of elements, \\ (iii) Write the elements a_{13}, a_{21}, a_{33}, a_{24}, a_{23} . \end{array}

Ans

(i) The order of matrix A is 3×4.

(ii) The number of elements in matrix A is 12.

(iii) The value of a₁₃ = 19, a₂₁ = 35, a₃₃ = – 5, a₂₄ = 12, a₂₃ = 5/2.

Q.2 If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

Ans

Possible order of matrix

1 × 24, 2 × 12, 3 × 8, 4 × 6, 6 × 4, 12 × 2, 24 × 1, 8 × 3.
Possible order for 13 elements: 1 × 13, 13 × 1.

Q.3 If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

Ans

Possible order for 18 elements

1 ×18, 2 × 9, 3 × 6, 6 × 3, 9 × 2, 18 × 1

Possible order for 5 elements = 1 × 5, 5 × 1.

Q.4

$\begin{array}{l} Constructa 2 \times 2 matrix, A = [a_{ij}], whose elementsare \\ givenby : (i) a_{ij} = \frac{{(i + j)}^{2}}{2} (ii) a_{ij} = \frac{i}{j} (iii) a_{ij} = \frac{{(i + 2 j)}^{2}}{2} \end{array}$

Ans

$\begin{array}{l} A = [a_{ij}] \\ (i) a_{ij} = \frac{{(i + j)}^{2}}{2} \\ A = (\begin{array}{l} a_{11} a_{12} \\ a_{21} a_{22} \end{array}) = (\begin{array}{l} 2 \frac{9}{2} \\ \frac{9}{2} 8 \end{array}) \\ (ii) a_{ij} = \frac{i}{j} \\ A = (\begin{array}{l} a_{11} a_{12} \\ a_{21} a_{22} \end{array}) = (\begin{array}{l} 1 \frac{1}{2} \\ 21 \end{array}) \\ (iii) a_{ij} = \frac{{(i + 2 j)}^{2}}{2} \\ A = (\begin{array}{l} a_{11} a_{12} \\ a_{21} a_{22} \end{array}) = (\begin{array}{l} \frac{9}{2} \frac{25}{2} \\ 818 \end{array}) \end{array}$

Q.5

$\begin{array}{l} Construct a 3 \times 4 matrix, whose elements are given by : \\ (i) a_{ij} = \frac{1}{2} | - 3 i + j | (ii) a_{ij} = 2 i - j \end{array}$

Ans

$\begin{array}{l} (i) aij = \frac{1}{2} | - 3 i + j | \\ A = [\begin{array}{l} a_{11} a_{12} a_{13} a_{14} \\ a_{21} a_{22} a_{23} a_{24} \\ a_{31} a_{32} a_{33} a_{34} \end{array}] \\ A = [\begin{array}{l} 1 \frac{1}{2} 0 \frac{1}{2} \\ \frac{5}{2} 2 \frac{3}{2} 1 \\ 4 \frac{7}{2} 3 \frac{5}{2} \end{array}] \\ (ii) a_{ij} = 2 i - j \\ A = [\begin{array}{l} a_{11} a_{12} a_{13} a_{14} \\ a_{21} a_{22} a_{23} a_{24} \\ a_{31} a_{32} a_{33} a_{34} \end{array}] \\ = [\begin{array}{l} 10 - 1 - 2 \\ 32 1 0 \\ 54 3 2 \end{array}] \end{array}$

Q.6

$\begin{array}{l} Find the values of x, y and z from the following equations : \\ (i) [\begin{array}{l} 4 3 \\ x 5 \end{array}] = [\begin{array}{l} y z \\ 1 5 \end{array}] \\ (ii) [\begin{array}{l} x + y 3 \\ 5 + z xy \end{array}] = [\begin{array}{l} 62 \\ 58 \end{array}] \\ (iii) [\begin{array}{l} x + y + z \\ x + z \\ y + z \end{array}] = [\begin{array}{l} 9 \\ 5 \\ 7 \end{array}] \end{array}$

Ans

$\begin{array}{l} (i) [\begin{array}{l} 4 3 \\ x 5 \end{array}] = [\begin{array}{l} y z \\ 1 5 \end{array}] \\ \Rightarrow x = 1, y = 4 and z = 3 \\ (ii) [\begin{array}{l} x + y 3 \\ 5 + z xy \end{array}] = [\begin{array}{l} 6 2 \\ 5 8 \end{array}] \\ \Rightarrow 5 + z = 5 \Rightarrow z = 5 - 5 = 0 \\ x + y = 6, and xy =8 \Rightarrow y = \frac{8}{x} \\ \Rightarrow x + y = 6 \\ x + \frac{8}{x} = 6 \\ \frac{x^{2} + 8}{x} = 6 \\ \Rightarrow x^{2} + 8 = 6 x \\ x^{2} - 6 x + 8 = 0 \Rightarrow x^{2} - 4 x - 2 x + 8 = 0 \\ \Rightarrow (x - 4) (x - 2) = 0 \\ \Rightarrow x = 2, 4 \\ If x = 2 then y = \frac{8}{2} = 4 \\ If x = 4 then y = \frac{8}{4} = 2 \\ (iii) [\begin{array}{l} x + y + z \\ x + z \\ y + z \end{array}] = [\begin{array}{l} 9 \\ 5 \\ 7 \end{array}] \\ x + y + z = 9 . .. (i) \\ x + z = 5 . .. (ii) \\ y + z = 7 . .. (iii) \\ From equation (i) and equation (ii), we have \\ y + 5 = 9 \Rightarrow y = 4 \\ From equation (i) and equation (iii), we have \\ x + 7 = 9 \Rightarrow x = 2 \\ From equation (i), we have \\ 2 + 4 + z = 9 \Rightarrow z = 9 - 6 = 3 \\ Thus, x = 2, y = 4 and z = 3 . \end{array}$

Q.7

$\begin{array}{l} Find the value of a, b, c and d from thee quation : \\ [\begin{array}{l} a - b 2 a + c \\ 2 a - b 3 c + d \end{array}] = [\begin{array}{l} - 1 5 \\ 0 13 \end{array}] \end{array}$

Ans

$\begin{array}{l} [\begin{array}{l} a - b 2 a + c \\ 2 a - b 3 c + d \end{array}] = [\begin{array}{l} - 1 5 \\ 0 13 \end{array}] \\ \Rightarrow a - b = - 1 . .. (i) \\ 2 a + c = 5 . .. (ii) \\ 2 a - b = 0 . .. (iii) \\ 3 c + d = 13 . .. (iv) \\ From equation (i) and equation (iii), we have \\ a = 1 and b = 2 \\ Putting value of a in equation (ii), we get \\ 2 (1) + c = 5 \Rightarrow c = 5 - 2 = 3 \\ Putting value of c in equation (iv), we get \\ 3 (3) + d = 13 \Rightarrow d = 13 - 9 = 4 \end{array}$

Q.8

\begin{array}{l} A = {[a_{ij}]}_{m \times n} is a square matrix, if \\ (A) m < n \\ (B) m > n \\ (C) m = n (D) None of these \end{array}

Ans

A is a square matrix if m=n.

So, option (C) is correction answer.

Q.9

\begin{array}{l} Which of the given values of x and y make the following \\ pair of matrice sequal \\ [\begin{array}{l} 3 x + 7 5 \\ y + 1 2 - 3 x \end{array}], [\begin{array}{l} 0 y - 2 \\ 8 4 \end{array}] \\ (A) x = - \frac{1}{3}, y = 7 (B) Not possiblet of ind \\ (C) y = 7, x = \frac{- 2}{3} (D) x = - \frac{1}{3}, y = \frac{- 2}{3} \end{array}

Ans

$\begin{array}{l} If both matrices are equal, then \\ [\begin{array}{l} 3 x +7 5 \\ y +1 2 -3 x \end{array}] = [\begin{array}{l} 0 y -2 \\ 8 4 \end{array}] \\ \Rightarrow 3 x + 7 = 0, y - 2 = 5 \\ and y + 1 = 8, 2 - 3 x = 4 \\ Then, x = - \frac{7}{3}, y = 7 and x = - \frac{2}{3} \\ Since, there are two different values of x, so it is difficult \\ to find the value of x to make matrices equal . \end{array}$

Q.10 The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is:

(A) 27

(B) 18

(D) 512

Ans

Number of elements is 9 and each element can be filled by 0 or 1.

The number of all possible matrices of order 3 x 3
with each entry 0 or 1 = 2⁹= 512

So, the option ‘D’ is correct.

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FAQs (Frequently Asked Questions)

1. Is it essential to practice all the questions of the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1?

Mathematics is a subject that requires a huge amount of practice and for scoring good

in the Mathematics Class 12 board examinations and having clarity of the concepts, the students must practice every question of the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1.

2. Are the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 difficult?

No, the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1are not difficult. Practising these solutions thoroughly will help the students to gain good marks in Class 12 Mathematics board examinations.

3. Is the NCERT Textbook enough to prepare the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1?

Yes, the NCERT Textbook is enough to strengthen the basic concepts of the students, so that they can solve any problem related to these concepts. Students should also practice sample papers and the past years’ papers for better preparation. Practising the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1help students to have a deep understanding of the concepts and eventually leads to better scores.

4. How can the students clear their doubts about the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1?

Students can refer to the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 provided by Extramarks, to clear their doubts. Also, students can subscribe to the Extramarks’ website and have access to learning tools like live doubt-solving classes, self-assessment, in-depth performance reports and much more. Students can also record their lectures for further assistance.

5. Are the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 available on Extramarks?

Yes, the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 are available on the Extramarks’ website. They are easily accessible as they are in PDF Format, and can also be downloaded on any device.

6. How many books are there in the curriculum of Class 12 Mathematics?

There are two volumes of NCERT Textbooks in the curriculum of Class 12 Mathematics. These books in themselves are enough for building the fundamentals for the students. This helps students to have strong concepts of Mathematics, ultimately leading to better scores.

7. Will the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 help students in any other competitive examination?

Yes, according to the changes in the admission pattern of Delhi University, the University is conducting entrance examinations that are entirely based on the content of NCERT. Also, there are other universities which follow the same pattern.

So yes, the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 will help students in the preparation for certain entrance examinations. Also, having a stronghold in Mathematics is very essential for the students who have to appear in the JEE examinations and for that the primary key is to be thorough with the NCERT Solutions.

8. Is it essential to practice the NCERT Exemplar questions to score well in Class 12 Mathematics board examinations?

Yes, students of Class 12 should practice every question that appears in front of them before sitting in the board examinations. Along with practising the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 students should also practice the NCERT Exemplar questions.

NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1 (Ex 3.1)

NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1 (Ex 3.1)

Access NCERT Solutions for Class 12 Maths Chapter 3 – Matrices

Matrices Class 12 NCERT Solutions 3.1 Available

NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1.

Step By Step Solutions For Class 12 Maths Chapter 3 Exercise 3.1

What is there In Class 12th NCERT Maths Chapter 3 Matrices Exercise 3.1?

Important Topics Covered under Class 12th NCERT Maths Chapter 3 Matrices Exercise 3.1

Importance of Class 12 Maths Chapter 3 Matrix

How can Extramarks NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.1 help you?

Get Solutions For The Complete Matrices Ex- 3.1 At One Place

One On One Interaction With Experts In Case You Find Any Doubts

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FAQs (Frequently Asked Questions)

1. Is it essential to practice all the questions of the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1?

2. Are the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 difficult?

3. Is the NCERT Textbook enough to prepare the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1?

4. How can the students clear their doubts about the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1?

5. Are the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 available on Extramarks?

6. How many books are there in the curriculum of Class 12 Mathematics?

7. Will the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 help students in any other competitive examination?

8. Is it essential to practice the NCERT Exemplar questions to score well in Class 12 Mathematics board examinations?

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NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1 (Ex 3.1)

NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1 (Ex 3.1)

Access NCERT Solutions for Class 12 Maths Chapter 3 – Matrices

Matrices Class 12 NCERT Solutions 3.1 Available

NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1.

Step By Step Solutions For Class 12 Maths Chapter 3 Exercise 3.1

What is there In Class 12th NCERT Maths Chapter 3 Matrices Exercise 3.1?

Important Topics Covered under Class 12th NCERT Maths Chapter 3 Matrices Exercise 3.1

Importance of Class 12 Maths Chapter 3 Matrix

How can Extramarks NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.1 help you?

Get Solutions For The Complete Matrices Ex- 3.1 At One Place

One On One Interaction With Experts In Case You Find Any Doubts

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FAQs (Frequently Asked Questions)

1. Is it essential to practice all the questions of the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1?

2. Are the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 difficult?

3. Is the NCERT Textbook enough to prepare the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1?

4. How can the students clear their doubts about the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1?

5. Are the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 available on Extramarks?

6. How many books are there in the curriculum of Class 12 Mathematics?

7. Will the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.1 help students in any other competitive examination?

8. Is it essential to practice the NCERT Exemplar questions to score well in Class 12 Mathematics board examinations?

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