Table of Contents
Subject specialists have created NCERT solutions for class 12 maths chapter 3, including thorough solutions for reference. These solutions are updated according to the latest term – I CBSE syllabus for 2021-22 and are provided in easy language for understanding. Tips and tricks are also provided.
These solutions are provided so a student can clear his doubts and get help with a deep understanding of the concept. Also, you can refer them to make the chapter notes and revisions notes. You can also download PDF from the link.
| Exercise 3.1 Class 12 Maths |
| Exercise 3.2 Class 12 Maths |
| Exercise 3.3 Class 12 Maths |
| Exercise 3.4 Class 12 Maths |
| Miscellaneous Exercise on Chapter 3 Class 12 |
NCERT Solutions for Class 12 Maths Chapter 3 Matrices
These NCERT Solutions include the following topics and subtopics. Students should practice problems on these topics to get ready for the term – I exam with the help of Infinity Learn.
3.1 Introduction
- In this chapter, students learned the fundamentals of matrix and matrix algebra and how matrices are associated with different fields.
3.2 Matrix
- 3.2.1 Order of a matrix
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- This portion clearly explains an easy example of how the elements are arranged to form a matrix and how its Order can be defined.
- This portion clearly explains an easy example of how the elements are arranged to form a matrix and how its Order can be defined.
3.3 Types of matrices
- 3.3.1 Equality of matrices
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- We learned about different types of matrices in this section, such as column matrix, row matrix, square matrix, diagonal matrix, scalar matrix, identity matrix, and zero matrices. Also, the equality of matrices is explained with examples.
- We learned about different types of matrices in this section, such as column matrix, row matrix, square matrix, diagonal matrix, scalar matrix, identity matrix, and zero matrices. Also, the equality of matrices is explained with examples.
3.4 Operations on Matrices
- 3.4.1 Addition of matrices
- 3.4.2 Multiplication of a matrix by a scalar
- 3.4.3 Properties of matrix addition
- 3.4.4 Properties of scalar multiplication of a matrix
- 3.4.5 Multiplication of matrices
- 3.4.6 Properties of multiplication of matrices
3.5 Transpose of a Matrix
- 3.5.1 Properties of the transpose of the matrices
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- The transposition of a matrix and properties are well explained with examples. These examples also prove the properties of the transpose of a matrix.
3.6 Symmetric and Skew Symmetric Matrices
- In this part, students will understand the definitions of symmetric and skew-symmetric matrices and the related theorems and examples.
3.7 Elementary Operation (Transformation) of a Matrix
- After going through this section, students will learn transformations on a matrix. There are six operations, i.e., transformations on a matrix. Three are due to columns, and three are due to rows, known as elementary operations or transformations.
3.8 Invertible Matrices
- 3.8.1 Inverse of a matrix by elementary operations
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- Here, students will understand the necessary conditions for matrices to have their inverse. Also, it has been given how to get an inverse matrix by performing elementary operations on the elements of a matrix.
The NCERT Solutions to questions provided by Infinity learn has covered all the below-mentioned properties and formulas.
- An ordered rectangular array of numbers or functions is called a matrix.
- A matrix with m rows and n columns is called a matrix of order m × n.
- [aij]m×1 is a column matrix.
- [aij]1×n is a row matrix.
- An m × n matrix is a square matrix if m=n.
- A = [aij]m×m is a diagonal matrix if aij=0, when i≠j.
- A = [aij]n×n is a scalar matrix if aij=0, when i≠j, aij=k (k is some constant), when i=j.
- A = [aij]n×n is an identity matrix if aij=1, when i=j, aij=0, when i≠j.
- A zero matrix has all its elements as zero.
- A = [aij] = [bij] = B if (i)A and B of the same order, (ii) aij = bij for all possible values of i and j.
- kA = k[aij]m×n = [k(aij)m×n]
- -A = (-1) A
- A – B = A + (-1) B
- A + B = B + A
- (A + B) + C = A + (B + C), where A, B and C are of the same order.
- k (A + B) = kA + kB, where A and B are of the same order, k is constant.
- (k + l) A = kA + lA, where k and l are constant.
The Frequently Asked Questions about NCERT Solutions in this chapter.
What are the main topics discussed in these NCERT Solutions?
In Mathematics, matrices are one of the easiest chapters; they are easy to understand. 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 main topics included in this chapter. These topics are discussed in easy language to help students score well in the first term exams irrespective of their intelligence quotient.
Why should we learn about matrices from NCERT Solutions in this chapter?
Matrices represent rectangular arrays of numbers which are represented in rows and columns. Using matrices, various mathematical operations like multiplication, addition, subtraction, and division can be done. Representing the data related to infant mortality rate, population, etc., are the widely used areas where matrices are used to simplify the complex data. The other known use of matrices is statistics, plotting graphs, and various scientific research purposes. The method of solving difficult linear equations is also made easy using the matrices.
Do these NCERT Solutions help you score well in the term – I exam?
This chapter includes all the important topics based on the latest update of CBSE guidelines. This chapter provides four exercises, giving the students numerous problems to solve independently. The solutions are made to boost the confidence in the minds of students before appearing for the term I exams. These solutions are thus helpful to score well for the term 1 exam.
