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NCERT Solutions for Exercise 3.3 Class 12 Maths Chapter 3 Matrices are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. In this article, you will get NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 which consists of questions related to the transpose of a matrix. If a matrix A of order m x n, then by interchanging the rows and columns of A we obtain the transpose of matrix A. Also, you will get questions related to p roperties of the transpose of the matrices, symmetric and skew-symmetric matrices in the exercise 3.3 class 12 maths. Only going through these class 12 maths ch 3 ex 3.3 solutions won't help you to understand the concept clearly. You should try to solve these class 12th maths chapter 3 exercise 3.3 questions on your own. You can take help from these solutions which are prepared by experts who know how best to answer in board exams.
12th class Maths exercise 3.3 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.
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Question 1(i). Find the transpose of each of the following matrices:
The transpose of the given matrix is
Question 1(ii). Find the transpose of each of the following matrices:
interchanging the rows and columns of the matrix A we get
Transpose is obtained by interchanging the rows and columns of matrix
Question 2(i). If and
, then verify
and
L.H.S :
R.H.S :
Thus we find that the LHS is equal to RHS and hence verified.
Question 2(ii). If and
, then verify
and
L.H.S :
R.H.S :
Hence, L.H.S = R.H.S. so verified that
.
Question 4. If and
, then find
:
Transpose is obtained by interchanging rows and columns and the transpose of A+2B is
Question 5(i) For the matrices A and B, verify that , where
,
To prove :
Hence, L.H.S =R.H.S
so it is verified that .
Question 5(ii) For the matrices A and B, verify that , where
,
To prove :
Heence, L.H.S =R.H.S i.e..
Question 6(i). If , then verify that
By interchanging rows and columns we get transpose of A
To prove:
L.H.S :
Question 6(ii). If , then verify that
By interchanging columns and rows of the matrix A we get the transpose of A
To prove:
L.H.S :
Question 7(i). Show that the matrix is a symmetric matrix.
the transpose of A is
Since, so given matrix is a symmetric matrix.
Question 7(ii) Show that the matrix is a skew-symmetric matrix.
The transpose of A is
Since, so given matrix is a skew-symmetric matrix.
Question 8(i). For the matrix , verify that
is a symmetric matrix.
We have
Hence , is a symmetric matrix.
Question 8(ii) For the matrix , verify that
is a skew symmetric matrix.
We have
Hence , is a skew-symmetric matrix.
Question 9. Find and
, when
the transpose of the matrix is obtained by interchanging rows and columns
Question 10(i). Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
Let
Thus, is a symmetric matrix.
Let
Thus, is a skew symmetric matrix.
Represent A as sum of B and C.
Let
Thus, is a symmetric matrix.
Let
Thus, is a skew-symmetric matrix.
Represent A as the sum of B and C.
Question 10(iii). Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
Let
Thus, is a symmetric matrix.
Let
Thus, is a skew-symmetric matrix.
Represent A as the sum of B and C.
Question 10(iv). Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
Let
Thus, is a symmetric matrix.
Let
Thus, is a skew-symmetric matrix.
Represent A as the sum of B and C.
Question 11 Choose the correct answer in the Exercises 11 and 12.
If A, B are symmetric matrices of same order, then AB – BA is a
(A) Skew symmetric matrix
(B) Symmetric matrix
(C) Zero matrix
(D) Identity matrix
If A, B are symmetric matrices then
and
we have,
Hence, we have
Thus,( AB-BA)' is skew symmetric.
Option A is correct.
Question 12 Choose the correct answer in the Exercises 11 and 12.
If and
, then the value of
is
(A)
(B)
(C)
(D)
Option B is correct.
NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 consists of 12 descriptive questions including two multiple choice type questions. Exercise 3.3 Class 12 Maths questions are related to finding the transpose of the matrices and the application of properties of transpose. There are 4 solved examples given before the NCERT textbook questions in the. First, try to solve these examples which will help you to get conceptual clarity. It will also help you in solving NCERT book problems easily as most of the textbook problems are related to solved examples.
Also Read| Matrices Class 12 Maths Chapter Notes
Also see-
Subject Wise NCERT Exampler Solutions
Happy learning!!!
NCERT solutions will help you to solve NCERT problems when you are not able to solve them on your own. For more questions NCERT exemplar problems will be useful. For CBSE board exam NCERT syllabus will be useful for exam preparation. Practice class 12 ex 3.3 to command the concepts.
The order of matrix having m rows and n columns is m x n.
If the transpose of matrix A is equal to matrix A then matrix A is a symmetric matrix.
If the transpose of matrix A is equal to the negative of matrix A then matrix A is a skew-symmetric matrix.
All the diagonal elements of a skew-symmetric matrix are zero.
(A')' = A
Hence the transpose of A' is matrix A.
If A is a symmetric matrix then A' = A.
If A is a symmetric matrix and k is a constant then (kA) ' = k (A)'
You can use them people also used problem
Hi,
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hello mahima,
If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.
hope this helps.
Hello Akash,
If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.
You can get the Previous Year Questions (PYQs) on the official website of the respective board.
I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
Thank you and wishing you all the best for your bright future.
Hello student,
If you are planning to appear again for class 12th board exam with PCMB as a private candidate here is the right information you need:
Remember
, these are tentative dates based on last year. Keep an eye on the CBSE website ( https://www.cbse.gov.in/ ) for the accurate and official announcement.
I hope this answer helps you. If you have more queries then feel free to share your questions with us, we will be happy to help you.
Good luck with your studies!
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