Open App

JEE Exam > JEE Videos > Mathematics (Maths) Class 12 > Transpose of a Matrix - Matrices

Transpose of a Matrix - Matrices Video Lecture | Mathematics (Maths) Class 12 - JEE

FAQs on Transpose of a Matrix - Matrices Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the transpose of a matrix?

Ans. The transpose of a matrix is a new matrix formed by interchanging its rows with columns. In other words, if the original matrix has dimensions m x n, the transpose will have dimensions n x m.

2. How do you find the transpose of a matrix?

Ans. To find the transpose of a matrix, you simply need to interchange its rows with columns. For each element in the original matrix, its corresponding element in the transpose will be at the position given by the column index of the original element as the row index and vice versa.

3. What are the properties of the transpose of a matrix?

Ans. The transpose of a matrix has the following properties: - The transpose of the transpose of a matrix is the original matrix. - The transpose of a sum of matrices is the sum of their transposes. - The transpose of a product of matrices is the product of their transposes in reverse order.

4. Can the transpose of a matrix be the same as the original matrix?

Ans. Yes, a matrix can be its own transpose if it is a symmetric matrix. A matrix is symmetric if it is equal to its transpose, i.e., A = A^T. Symmetric matrices have interesting properties and are widely used in various mathematical applications.

5. How does the transpose of a matrix affect its determinants and eigenvalues?

Ans. The transpose of a matrix does not change its determinants. In other words, if the original matrix has a determinant value of x, the transpose will also have a determinant of x. However, the eigenvalues of a matrix and its transpose are the same. The eigenvalues represent the scaling factors of the eigenvectors, and they remain unchanged when the matrix is transposed.

About this Video

4.96/5 Rating

Oct 23, 2025 Last updated

Related Exams

JEE Commerce Humanities/Arts Grade 12 CUET

Video Description: Transpose of a Matrix - Matrices for JEE 2025 is part of Mathematics (Maths) Class 12 preparation. The notes and questions for Transpose of a Matrix - Matrices have been prepared according to the JEE exam syllabus. Information about Transpose of a Matrix - Matrices covers all important topics for JEE 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Transpose of a Matrix - Matrices.

Introduction of Transpose of a Matrix - Matrices in English is available as part of our Mathematics (Maths) Class 12 for JEE & Transpose of a Matrix - Matrices in Hindi for Mathematics (Maths) Class 12 course. Download more important topics related with notes, lectures and mock test series for JEE Exam by signing up for free.

Description

Video Lecture & Questions for Transpose of a Matrix - Matrices Video Lecture | Mathematics (Maths) Class 12 - JEE - JEE full syllabus preparation | Free video for JEE exam to prepare for Mathematics (Maths) Class 12.

Information about Transpose of a Matrix - Matrices

Here you can find the meaning of Transpose of a Matrix - Matrices defined & explained in the simplest way possible. Besides explaining types of Transpose of a Matrix - Matrices theory, EduRev gives you an ample number of questions to practice Transpose of a Matrix - Matrices tests, examples and also practice JEE tests.

	Mathematics (Maths) Class 12 223 videos\|377 docs\|167 tests

Mathematics (Maths) Class 12

223 videos|377 docs|167 tests

Join Course for Free

Explore Courses for JEE exam