 # NCERT Solutions for Class 12 Maths Chapter 3 Matrices

## NCERT Solutions For Class 12 Maths Chapter 3 PDF Free Download

NCERT Solutions for class 12 Maths chapter 3 – Matrices, provides solutions for all the questions enlisted under the chapter (All Exercises and Miscellaneous Exercise solutions). Class 12 maths NCERT Solutions are solved by maths experts using step by step approach under the guidelines of NCERT to assists students in their examination. This topic is extremely important for both CBSE board exam and for competitive exams. Students can practice these questions and improve their skills. Download free NCERT Solutions pdf now and excel your knowledge.

## Access Answers of Maths NCERT Chapter 3 Matrices                                                                            Also Access NCERT Exemplar for Class 12 Maths Chapter 3 CBSE Notes for Class 12 Maths Chapter 3

### NCERT Solutions for Class 12 Maths Chapter 3 Matrices

In Class 12 maths Chapter 3, students will deal with matrices and their types, properties, order of a matrix , operations on matrices (addition, multiplication), transpose of matrix, symmetric and skew-symmetric matrices, elementary operation (transformation) of a matrix, invertible matrices and inverse of a matrix by elementary operations. Students can practice problems on these topics and get ready for the exam.

The Summary of this chapter are as follows:

• An ordered rectangular array of number or functions is called a matrix.
• A matrix which has 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 a 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 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 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.

NCERT Solutions For Class 12 Maths Chapter 3 Exercises:

Get a detailed solution for all the questions listed under the below exercises:

Exercise 3.1 Solutions : 10 Questions (7 Short Answers, 3 MCQ)

Exercise 3.2 Solutions : 22 Questions(14 Long, 6 Short, 2 MCQ)

Exercise 3.3 Solutions : 12 Questions (10 Short Answers, 2 MCQ)

Exercise 3.4 Solutions : 18 Questions (4 Long, 13 Short, 1 MCQ)

Miscellaneous Exercise Solutions: 15 Questions (7 Long, 5 Short, 3 MCQ)

### NCERT Solutions for Class 12 Maths Chapter 3 Matrices

The main topics covered NCERT Solutions for Class 12, Chapter 3- Matrices are:

 Exercise Topic 3.1 Introduction 3.2 Matrix 3.3 Types of Matrices 3.4 Operations on Matrices 3.5 Transpose of a Matrix 3.6 Symmetric and Skew Symmetric Matrices 3.7 Elementary Operation (Transformation) of a Matrix 3.8 Invertible Matrices Others Miscellaneous Q&A

### Key Features of NCERT Solutions for Class 12 Maths Chapter 3 Matrices

1. NCERT Solutions will help the students to strengthen their basics.
2. All exercises meticulously solved by subject experts.
3. Step by step solutions for all the questions.
4. NCERT Solutions will help in boosting the student confidence level.
5. NCERT solutions are valuable aid for the students in their assignments and competitive exams.