NCERT Solutions for Class 12 Maths Chapter 3.4 Matrices

NCERT Exercise 3.4 Class 12 Maths Solutions: NCERT Exercise 3.4 Class 12th Solutions deal with a significant chapter called ‘Matrices’. Matrices are used in various branches of Mathematics and are the result of attempts to obtain compact and simple methods of solving systems of linear equations. While solving the in-text questions of every chapter, students need to refer to the NCERT Class 12 Maths Solutions. 

CBSE Class 12 Maths Chapter 3.4 deals with Elementary Operation (Transformation) of a Matrix, Invertible Matrices. and the Inverse of a Matrix by Elementary Operations. Embibe offers over 400 practice questions for all sub-topics present in Chapter 3 Matrices of Class 12 Maths. Students must place their primary focus on practising all the in-text questions offered by Embibe. Keep scrolling to access the NCERT solutions for Class 12 Maths Chapter 3 Exercise 3.4.

NCERT Solutions for Class 12 Maths Chapter 3.4: Important Topics

Matrices is a unique concept that grows interesting as students keep exploring and solving the questions. Once the concept of problem-solving is understood, students can easily go ahead and solve easy and complicated problems as well. Students must keep in mind that they should learn the basics well. This helps them to handle any type of question asked in the exam.

Embibe delivers solutions to all the questions provided in Class 12 Maths Chapter 3.4 based on the latest syllabus. Moreover, all the solutions are made available for by Embibe to help students score good marks in the exams. Not just NCERT solutions, Embibe also offers NCERT 3D Videos, NCERT Exemplars, Embibe Explainers, etc., for.

Before we move on to exercise 3.4 NCERT solutions, let us know the list of important topics present in the Matrices chapter. Students can refer to the below table to get a quick idea of the important topics.

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

Below-mentioned are some of the important points related to CBSE Maths Class 12 Chapter 3.

• A matrix having only one row is called a row matrix.
• A matrix having only one column is called a column matrix.
• Commutativity: If A and B are two matrices of the same order, then A+B=B+A.
• Associativity: If A, B, C are three matrices of the same order, then (A+B)+C=A+(B+C).
• Existence of Identity: The null matrix is the identity element for matrix addition i.e., A+O=A=O+A
• Cancellation Laws: If A, B, C are three matrices of the same order, then A+B=A+C⇒B=C and, B+A=C+A⇒B=C.
• Properties of scalar multiplication of matrices: If A,B are two matrices of the same order and k,lk,l are scalars, then
  (a) k(A+B)=kA+kB
  (b) (k+l)A=kA+lA
  (c) (kl)A=k(lA)=l(kA)
  (d) (−k)A=−(kA)=k(−A)
• 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) A matrix obtained from an identity matrix by a single elementary operation is called an elementary matrix.
  (ii) Adding to the elements of a row (column), the corresponding elements of any other row (column) multiplied by any scalar.
• 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
  (ii) We perform a sequence of elementary row operations successively on A on the LHS and the pre-factor I on RHS till we obtain. The matrix B, so obtained, is the desired inverse of matrix A.

NCERT Solutions for Class 12 Maths: All Chapters

The detailed NCERT Class 12 Maths solutions for all the chapters are provided below for your reference:

• 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 Matrices

Q.1: Why should I refer to Embibe’s NCERT Solutions for Class 12 Maths?
Ans: Students should refer to Embibe’s Class 12 NCERT Maths solutions because these solutions are compiled by top academic experts. Every question contains the latest and step-by-step explanation which helps students understand even the most difficult sum. 

Q.2: Where can I get the Matrices Class 12 NCERT solutions online?
Ans: Students can get the Matrices Class 12 NCERT solutions from this article or by visiting Embibe.

Q.3: Are Embibe’s exercise 3.4 Class 12 Maths solutions?
Ans: Yes, the NCERT Class 12 Maths solutions provided by Embibe are completely. Students can access them anytime online and save the study materials to study offline.

Q.4: Which is the best online app for Class 12 Maths NCERT solutions?
Ans: Embibe: The Learning Outcomes app is the best app for CERT Class 12 Maths Solutions. 

Q.5: What are the topics in Chapter 3 Maths Class 12?
Ans: Students shall study Matrix, types of matrices, operations on matrices, transpose of a matrix, symmetric and skew-symmetric matrices, elementary operation on matrix, and invertible matrices in Chapter 3 Maths Class 12.