NCERT Solutions for Class 9 Political Science Chapter 2

August 8, 202239 Insightful Publications

**NCERT Solutions for Class 12 Maths Chapter 3:** As Class 12 board exams are a turning point in a student’s life, NCERT Solutions for Class 12 maths chapters can help students in their preparation. In this article, students can find a direct link to the Class 12 NCERT Solutions Maths Chapter 3 PDF. It is critical for students to go through matrices and NCERT solutions for better performance in matrices chapter 3 during class 12 board exams.

Matrices are regarded as a mark-earning chapter in both board and entrance examinations. Embibe provides Class 12 Maths Chapters 3 Solutions that students can use to supplement their preparation and significantly improve their scores. Continue reading this article to download the Class 12 Chapter 3 Maths NCERT solutions.

Before knowing the NCERT solutions for chapter 3 of Class 12 Maths, let us have an overview of all the topics of the chapter. There are three exercises under this chapter. The topics and sub-topics included in the Class 12th maths matrices chapter are tabulated below:

1 | Introduction |

2 | Matrix |

3 | Order of a matrix |

4 | Types of Matrices |

5 | Equality of matrices |

6 | Operations on Matrices |

7 | Addition of matrices |

8 | Multiplication of a matrix by a scalar |

9 | Properties of matrix addition |

10 | Properties of scalar multiplication of a matrix |

11 | Multiplication of matrices |

12 | Properties of multiplication of matrices |

13 | Transpose of a Matrix |

14 | Properties of transpose of the matrices |

15 | Symmetric and Skew-Symmetric Matrices |

16 | Elementary Operation (Transformation) of a Matrix |

17 | Invertible Matrices |

18 | Inverse of a matrix by elementary operations |

Students can find the NCERT solutions for all the questions of chapter 3 of Class 12 Maths below. By practicing the answers for these questions, students can confidently approach any kind of question asked in the exam. Moreover, they become confident and proficient in the concepts.

>Here are a few questions and solutions from Class 12 Maths Chapter 3 NCERT solutions that a student can go through:

**Q.1. If the order of the matrix A=2519-735-2521231-517 is m×n, then m+n=7**

**Solution: **Given matrix: A=2519-735-2521231-517

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

Here, the matrix has 3 rows and 4 columns Therefore, order of matrix A=3×4 So, m+n=3+4=7

**Q.2. Find the number of elements in the matrix A=2519-735-2521231-517.**

**Solution: **Given matrix: A=2519-735-2521231-517.

We can count that number of elements is 12.

Alternatively, if the matrix has order m×n, then it has m·n number of elements.

Here, the order of matrix is 3×4.

So, number of elements=3·4=12.

**Q.3. In the matrix A=2519-735-2521231-517, find the sum of elements a13, a21, a33 and a24.**

**Solution**: In general, aij is an element lying in the ith row and jth column.

Here, A=2519-735-2521231-517

Therefore, a13 is an element lying in the first row, third column. ∴ a13=19 a21 is an element lying in the second row, first column. ∴ a21=35 a33 is an element lying in the third row, third column. ∴ a33=-5 a24 is an element lying in the second row, fourth column. ∴ a24=12 Now, sum of elements =19+35-5+12=61

**DOWNLOAD MATRICES NCERT SOLUTIONS PDF**

Some important questions from 12th Maths matrices are given below:

The knowledge of Matrices is necessary for various branches of Mathematics. Matrix is an important chapter for all Science subjects. Students need to focus on understanding the basic concepts associated with this chapter to master this topic.

This mathematical tool simplifies our work to a great extent when compared with other straightforward methods. The evolution of the concept of matrices is the result of an attempt to obtain compact and simple methods of solving the system of linear equations.

Matrices are used for the representation of the coefficients in different systems of linear equations, however, the utility of matrices. Matrix notation and operations are used in electronic spreadsheet programs for personal computers, which in turn are used in different areas of business and science like budgeting, sales projection, cost estimation, analyzing the results of an experiment, etc.

Also, many physical operations such as magnification, rotation, and reflection through a plane can be represented mathematically by matrices. Matrices are also used in cryptography. This mathematical tool is not only used in certain branches of Sciences, but also in Genetics, Economics, Sociology, Modern Psychology and Industrial Management.

In this chapter, you will learn about the fundamentals of matrix and matrix algebra along with Class 12 Maths NCERT solutions Chapter 3 Matrices.

**Q.1: Where can I find NCERT Solutions for Matrices topic of Class 12 Chapter 3 online? ****Ans**: You can find Class 12 Maths Chapter 3 Matrices solutions PDF/Matrices Class 12 NCERT Solutions PDF for free on Embibe.

**Q.2: Are the NCERT 12th Maths Chapter 3 solutions provided by Embibe free?****Ans**: Yes, all NCERT solutions, for all classes provided by Embibe are free to download. You do not even have to register or signup to access the PDFs.

**Q.3: Where can I solve NCERT Class 12 Maths Chapter 3 questions online?****Ans**: You can solve free CBSE Class 12 Maths Chapter 3 questions on Embibe. All questions come with detailed solutions.

**Q.4: Are Matrices of Class 12 Maths Chapter 3 the easiest topic?****Ans**: Yes, Class 12 Maths Chapter 3 is one of the easiest chapters of the Maths syllabus and can be easily prepared with the help of Class 12 Maths Chapter 3 NCERT solutions.

**Q.5: What are the Matrices topics in Class 12 Maths Chapter 3? ****Ans**: Matrix, types of matrices, operations on matrices, transpose of a matrix, symmetric and skew-symmetric matrices, elementary operation on matrix, and invertible matrices are the topics discussed in Class 12 Maths Chapter 3 Exercise 3.1, 3.2, and more.

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