NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise: Matrices is the third chapter in the NCERT Class 12 Maths textbook and constitutes an important part of the Maths syllabus. Matrices Class 12 NCERT Solutions Chapter 3 Miscellaneous Exercise will help students strengthen their grasp on the chapter and prepare better for the board exam.

CBSE Class 12 Maths Chapter 3 is based on the topics namely Order and Types of Matrices, Addition, Operations and Equality of Matrices, Invertible Matrices, Multiplication of Matrices and many more. Embibe offers more than 400 practice questions for all the sub-topics present in the Matrices chapter. Students must ensure that they practice all the in-text questions offered by Embibe to score maximum marks in the exams. Keep reading to know NCERT solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise.

NCERT Solutions for Class 12 Maths Chapter 3: Important Topics

Matrices is one of the most interesting topics of Class 12 Maths. Students are required to understand the basics first to get a deeper level understanding of the problems. It is advisable for the students to start with easy and basic problems first so that they can become prepared to answer the questions of a difficult level.

Once, the students are able to arrive at the solutions easily, problem-solving becomes easy and students will develop the capability to answer any type of question asked in the exam. At Embibe, students can access the solutions to all the questions provided in Class 12 Maths textbooks for and they are based on the latest syllabus. Also, students can practice NCERT 3D Videos, NCERT Exemplars, Embibe Explainers, etc., for.

Students can access the list of topics included in CBSE Class 12 Maths Chapter 3 from below:

NCERT Solutions for Class 12 Maths Chapter 3: Points to Remember

• Introduction to Matrices: A set of numbers (real or imaginary) or symbols or expressions arranged in the form of a rectangular array of m rows and n columns is called m×n matrix.
• Types of Matrices:
  (i) A matrix having only one row is called a row matrix.
  (ii) A matrix having only one column is called a column matrix.
  (iii) A matrix in which the number of rows is equal to the number of columns, say n, is called a square matrix of order n.
• The elements aij of a square matrix A=[aij]n×n for which i=j i.e. the elements a11,a22,….,ann are called the diagonal elements and the line along which they lie is called the principal diagonal or leading diagonal.
• A square matrix A=[aij]n×n is called a diagonal matrix if all the elements, except those in the leading diagonal, are zero i.e. aij=0 for i≠j.
• All main diagonal elements of a skew–symmetric matrix are zero.
• Every square matrix can be uniquely expressed as the sum of a symmetric and a skew–symmetric matrix.
• All positive integral powers of a symmetric matrix are symmetric matrices.
• All odd positive integral powers of a skew–symmetric matrix are skew–symmetric matrices.
• Elementary operations (transformation) of a matrix.
  (i) Interchange of any two rows (columns).
  (ii) Multiplying all elements of a row (column) of a matrix by a non-zero scalar.
  (iii) Adding to the elements of a row (column), the corresponding elements of any other row (column) multiplied by any scalar.
  (iv) A matrix obtained from an identity matrix by a single elementary operation is called an elementary matrix.
• Inverse of a matrix by elementary operations
  (i) In order to find the inverse of a non-singular square matrix A by elementary operations, we write A=IA or A=AI

NCERT Solutions for Class 12 Maths: All Chapters

Students can find the detailed NCERT Class 12 Maths solutions for all the chapters as provided below:

• Chapter 1: Relations and Functions
• Chapter 2: Inverse Trigonometric Functions
• Chapter 4: Determinants
• Chapter 5: Continuity and Differentiability
• Chapter 6: Applications of Derivatives
• Chapter 7: Integrals
• Chapter 8: Application of Integrals
• Chapter 9: Differential Equations
• Chapter 10: Vector Algebra
• Chapter 11: Three Dimensional Geometry
• Chapter 12: Linear Programming

FAQs on NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise

Q.1: Where can I download NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise?
Ans: NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise can be downloaded from Embibe.

Q.2: What are Matrices?
Ans: Matrices are arrays of numbers, expressions or symbols arranged in rows and columns that are used for representing mathematical objects. They are applied across various disciplines including genetics, economics and industrial management.

Q.3: Is NCERT Class 12 Maths Chapter 3 Matrices the easiest chapter?
Ans: NCERT Class 12 Maths Chapter 3 Matrices is not the easiest chapter but one of the easier ones as it mostly deals with the introduction and basics of Matrices. It is very important though as the concept is important for competitive exams and technical courses like engineering.

Q.4: What are the topics included in NCERT Class 12 Maths Chapter 3 Matrices?
Ans: The topics in NCERT Class 12 Maths Chapter 3 Matrices are Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, Linear Programming and Probability.

Q.5: How are NCERT Solutions for Class 12 Maths helpful?
Ans: NCERT Solutions for Class 12 Maths are very helpful for students for the following reasons:

• They are a very good way for students to revise concepts that they’ve learnt
• The solutions provide step-wise guidance on how to prepare answers in exams
• They are very helpful for competitive exams like JEE and BITSAT.