JEE Exam > JEE Videos > Mathematics (Maths) for JEE Main & Advanced > How to Calculate the Adjoint of a matrix?
How to Calculate the Adjoint of a matrix? Video Lecture | Mathematics (Maths) for JEE Main & Advanced
FAQs on How to Calculate the Adjoint of a matrix? Video Lecture - Mathematics (Maths) for JEE Main & Advanced
| 1. How do I calculate the adjoint of a matrix? |  |
To calculate the adjoint of a matrix, follow these steps:
1. Find the cofactor of each element in the matrix. The cofactor of an element is the determinant of the submatrix obtained by removing the row and column containing that element.
2. Create a new matrix called the cofactor matrix, where each element is replaced by its corresponding cofactor.
3. Transpose the cofactor matrix by interchanging its rows with columns to obtain the adjoint matrix.
For example, let's say we have a 3x3 matrix A:
A = | a11 a12 a13 |
| a21 a22 a23 |
| a31 a32 a33 |
The adjoint of A, denoted as adj(A), can be calculated by finding the cofactor matrix and then transposing it.
| 2. What is the purpose of calculating the adjoint of a matrix? | |
The adjoint of a matrix is often used to find the inverse of a matrix. If a matrix A is invertible (non-singular), then its inverse A^-1 can be obtained by dividing the adjoint of A by the determinant of A. In other words, A^-1 = adj(A) / det(A). The adjoint is also useful in solving systems of linear equations and in various applications of linear algebra.
| 3. Can the adjoint of a matrix be equal to the original matrix? | |
No, the adjoint of a matrix is not equal to the original matrix unless the original matrix is an orthogonal matrix. An orthogonal matrix is a square matrix where the transpose of the matrix is equal to its inverse. In such cases, the adjoint and the original matrix are the same.
| 4. Is the adjoint of a matrix always a square matrix? | |
Yes, the adjoint of a matrix is always a square matrix, regardless of the size or dimensions of the original matrix. If the original matrix is an m x n matrix, then its adjoint will be an n x m matrix.
| 5. Can the adjoint of a matrix be negative? | |
No, the adjoint of a matrix cannot be negative. The adjoint matrix contains the cofactors of the original matrix, and a cofactor is a determinant. Determinants are always non-negative values, so the adjoint matrix will also have non-negative elements.
About this Video
4.71/5
Rating
Sep 04, 2025
Last updated
Related Exams
Video Description: How to Calculate the Adjoint of a matrix? for JEE 2025 is part of Mathematics (Maths) for JEE Main & Advanced preparation.
The notes and questions for How to Calculate the Adjoint of a matrix? have been prepared according to the JEE exam syllabus.
Information about How to Calculate the Adjoint of a matrix? covers all important topics for JEE 2025 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for How to Calculate the Adjoint of a matrix?.
Introduction of How to Calculate the Adjoint of a matrix? in English is available as part of our Mathematics (Maths) for JEE Main & Advanced for JEE & How to Calculate the Adjoint of a matrix? in
Hindi for Mathematics (Maths) for JEE Main & Advanced 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 How to Calculate the Adjoint of a matrix? Video Lecture | Mathematics (Maths) for JEE Main & Advanced - JEE full syllabus preparation | Free video for JEE exam to prepare for Mathematics (Maths) for JEE Main & Advanced.
Information about How to Calculate the Adjoint of a matrix?
Here you can find the meaning of How to Calculate the Adjoint of a matrix? defined & explained in the simplest way possible.
Besides explaining types of How to Calculate the Adjoint of a matrix? theory, EduRev gives you an ample number of questions to practice How to Calculate the Adjoint of a matrix? tests,
examples and also practice JEE tests.
Related Searches
Semester Notes
,Exam
,study material
,mock tests for examination
,Free
,Previous Year Questions with Solutions
,past year papers
,How to Calculate the Adjoint of a matrix? Video Lecture | Mathematics (Maths) for JEE Main & Advanced
,Sample Paper
,video lectures
,How to Calculate the Adjoint of a matrix? Video Lecture | Mathematics (Maths) for JEE Main & Advanced
,MCQs
,Important questions
,How to Calculate the Adjoint of a matrix? Video Lecture | Mathematics (Maths) for JEE Main & Advanced
,practice quizzes
,Objective type Questions
,shortcuts and tricks
,ppt
,Viva Questions
,Summary
,Extra Questions
;
Study How to Calculate the Adjoint of a matrix? on the App
Students of JEE can study How to Calculate the Adjoint of a matrix? alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the How to Calculate the Adjoint of a matrix?,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of How to Calculate the Adjoint of a matrix? is prepared as per the latest JEE syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily