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Given a matrix A such that
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
L.H.S :
R.H.S :
Thus we find that the LHS is equal to RHS and hence verified.
Question 2(ii). If
L.H.S :
R.H.S :
Hence, L.H.S = R.H.S. so verified that
Question 4. If
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
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
To prove :
Hence, L.H.S =R.H.S i.e.
Question 6(i). If
By interchanging rows and columns, we get the transpose of A
To prove:
L.H.S :
Question 6(ii). If
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
The transpose of A is
Since
Question 7(ii) Show that the matrix
The transpose of A is
Since
Question 8(i). For the matrix
We have
Hence,
Question 8(ii) For the matrix
We have
Hence,
Question 9. Find
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,
Let
Thus,
Represent A as the sum of B and C.
Let
Thus,
Let
Thus,
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,
Let
Thus,
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,
Let
Thus,
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 the 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
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
(A)
(B)
(C)
(D)
Option B is correct.
Also Read,
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
Also, read,
These links lead to NCERT textbook solutions for other subjects. Students can check and analyse these well-structured solutions for a deeper understanding.
Students may visit these NCERT exemplar links for additional practice.
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)'
Admit Card Date:06 May,2025 - 20 May,2025
Admit Card Date:06 May,2025 - 20 May,2025
Application Date:07 May,2025 - 17 May,2025
Changing from the CBSE board to the Odisha CHSE in Class 12 is generally difficult and often not ideal due to differences in syllabi and examination structures. Most boards, including Odisha CHSE , do not recommend switching in the final year of schooling. It is crucial to consult both CBSE and Odisha CHSE authorities for specific policies, but making such a change earlier is advisable to prevent academic complications.
Hello there! Thanks for reaching out to us at Careers360.
Ah, you're looking for CBSE quarterly question papers for mathematics, right? Those can be super helpful for exam prep.
Unfortunately, CBSE doesn't officially release quarterly papers - they mainly put out sample papers and previous years' board exam papers. But don't worry, there are still some good options to help you practice!
Have you checked out the CBSE sample papers on their official website? Those are usually pretty close to the actual exam format. You could also look into previous years' board exam papers - they're great for getting a feel for the types of questions that might come up.
If you're after more practice material, some textbook publishers release their own mock papers which can be useful too.
Let me know if you need any other tips for your math prep. Good luck with your studies!
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I hope this information helps you.
Hi,
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Age: As of the last registration date, you must be between the ages of 16 and 40.
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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.
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