NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 Matrices
NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3: Get inside detail NCERT Solutions for Class 12 Maths Chapter 3-Matrices Exercise 3.3 prepared by academic team of Physics Wallah all questions are solved in detail
Krati Saraswat10 Jan, 2024
Share
NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 Matrices
NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 Matrices is prepared by academic team of Physics Wallah. We have prepared NCERT Solutions for all exercise of chapter 3. Given below is step by step solutions of all questions given in NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 Matrices.NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise
NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3
Solve The Following Questions NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 Matrices
Question 1. Find the transpose of each of the following matrices: (i)
(ii)
(iii)
Solution :
(i) Let A =
Transpose of A = A’ or A
T
= [ 5 1/2 -1]
(ii)
Transpose of A = A’ or A
T
=
(iii)
Transpose of A = A’ or A
T
=
NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1
Question 2. If
then verify that:
(i)
(A + B)' = A' + B'
(ii)
(A - B)' = A' - B'
Solution :
NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.2
Question 3. If
then verify that:
(i)
(A + B)' = A' + B'
(ii)
(A - B)' = A' - B'
Solution :
NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4
Question 4. If
then find (A + 2B)’.
Solution :
(ii)
Solution :
| NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1 | NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.2 |
| NCERT Solutions for Class 12 Maths Chapter 2 Miscellaneous Exercise | |
then verify that A’A = I.
(ii) If A =
then verify that A’A = I.
Solution :
Question
7. (i) Show that the matrix A =
is a symmetric matrix.
(ii) Show that the matrix A =
is a skew symmetric matrix.
Solution :
(i) Given: A =
Changing rows of matrix A as the columns of new matrix A’ =
= A
∴ A’ = A
Therefore, by definitions of symmetric matrix, A is a symmetric matrix.
(ii) Given: A =
A’ =
=
-
= - A
∴ A’ = - A
Therefore, by definition matrix A is a skew-symmetric matrix
Question
8. For a matrix A =
verify that:
(i) (A + A’) is a symmetric matrix.
(ii) (A – A’) is a skew symmetric matrix.
Solution :
Question
9. Find 1/2 (A + A’) and 1/2(A – A’) when A =
Solution :
Question
10. Express the following matrices as the sum of a symmetric and skew symmetric matrix:
(i)
(ii)
(iii)
(iv)
Solution :
.png)
(iii)
(iv)
Choose the correct answer in Exercises 11 and 12.
Question 11. If A and B are symmetric matrices of same order, AB – BA is a: (A) Skew-symmetric matrix (B) Symmetric matrix (C) Zero matrix (D) Identity matrix Solution : Given: A and B are symmetric matrices ∴ A = A’ and B = B’ Now, (AB – BA)’ = (AB)’ – (BA)’ ∴ (AB – BA)’ = B’A’ – A’B’ [Reversal law] ∴ (AB – BA)’ = BA – AB [From eq. (i)] ∴ (AB – BA)’ = – (AB – BA) ∴ (AB – BA) is a skew matrix. Therefore, option (A) is correct. Question 12. If A =
, then A + A’ = I, if the value of
α is:
(A) π/6
(B) π/3
(C)
π
(D) 3
π/2
Solution :
Therefore, option (B) is correct.
Talk to a counsellorHave doubts? Our support team will be happy to assist you!
Check out these Related Articles
Join 15 Million students on the app today!
Live & recorded classes available at easeDashboard for progress trackingMillions of practice questions at your fingertips
Free Learning Resources
PW Books
Notes (Class 10-12)
PW Study Materials
Notes (Class 6-9)
Ncert Solutions
Govt Exams
Class 6th to 12th Online Courses
Govt Job Exams Courses
UPSC Coaching
Defence Exam Coaching
Gate Exam Coaching
Other Exams
Know about Physics Wallah
Physics Wallah is an Indian edtech platform that provides accessible & comprehensive learning experiences to students from Class 6th to postgraduate level. We also provide extensive NCERT solutions, sample paper, NEET, JEE Mains, BITSAT previous year papers & more such resources to students. Physics Wallah also caters to over 3.5 million registered students and over 78 lakh+ Youtube subscribers with 4.8 rating on its app.
We Stand Out because
We provide students with intensive courses with India’s qualified & experienced faculties & mentors. PW strives to make the learning experience comprehensive and accessible for students of all sections of society. We believe in empowering every single student who couldn't dream of a good career in engineering and medical field earlier.
Our Key Focus Areas
Physics Wallah's main focus is to make the learning experience as economical as possible for all students. With our affordable courses like Lakshya, Udaan and Arjuna and many others, we have been able to provide a platform for lakhs of aspirants. From providing Chemistry, Maths, Physics formula to giving e-books of eminent authors like RD Sharma, RS Aggarwal and Lakhmir Singh, PW focuses on every single student's need for preparation.
What Makes Us Different
Physics Wallah strives to develop a comprehensive pedagogical structure for students, where they get a state-of-the-art learning experience with study material and resources. Apart from catering students preparing for JEE Mains and NEET, PW also provides study material for each state board like Uttar Pradesh, Bihar, and others
Copyright © 2025 Physicswallah Limited All rights reserved.