Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > eAdenotes the exponential of a square matrix ...
Start Learning for Free
eA denotes the exponential of a square matrix A. Suppose λ is an eigen value and v is the corresponding eigen-vector of matrix A.
Consider the following two statements :
Statement 1 : eλ is an eigen value of eA .
Statement 2 : v is an eigen-vector of eA.
Which one of the following options is correct?
- a)Statement 1 is true and statement 2 is false.
- b)Statement 1 is false and statement 2 is true.
- c)Both the statements are correct.
- d)Both the statements are false.
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
eAdenotes the exponential of a square matrix A. Suppose λ is an...
We have a square matrix A. The exponential of matrix A, denoted as e^A, is defined as the sum of the infinite series:
e^A = I + A + (A^2 / 2!) + (A^3 / 3!) + ...
where I is the identity matrix and A^k represents the matrix A raised to the power of k.
The exponential of a matrix has various properties, including:
1. e^0 = I, where 0 is the zero matrix and I is the identity matrix.
2. If A and B commute (AB = BA), then e^(A + B) = e^A * e^B.
3. If A is invertible, then e^(-A) = (e^A)^(-1).
The exponential of a matrix can be calculated using a variety of methods, such as the Taylor series expansion, diagonalization, or using the Jordan canonical form.
e^A = I + A + (A^2 / 2!) + (A^3 / 3!) + ...
where I is the identity matrix and A^k represents the matrix A raised to the power of k.
The exponential of a matrix has various properties, including:
1. e^0 = I, where 0 is the zero matrix and I is the identity matrix.
2. If A and B commute (AB = BA), then e^(A + B) = e^A * e^B.
3. If A is invertible, then e^(-A) = (e^A)^(-1).
The exponential of a matrix can be calculated using a variety of methods, such as the Taylor series expansion, diagonalization, or using the Jordan canonical form.
Free Test
FREE
| Start Free Test |
Community Answer
eAdenotes the exponential of a square matrix A. Suppose λ is an...
Given λ is an eigen value of A.
∴ Statement (1) is true.
We know that eigen vector of A and polynomial matrix in A is same.
=> Eigen vector of A and eA is same.
∴ Statement (2) is true.
∴ Statement (2) is true.
Attention Electrical Engineering (EE) Students!
To make sure you are not studying endlessly, EduRev has designed Electrical Engineering (EE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Electrical Engineering (EE).
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Similar Electrical Engineering (EE) Doubts
Top Courses for Electrical Engineering (EE)View all
eAdenotes the exponential of a square matrix A. Suppose λ is an eigen value and v is the corresponding eigen-vector of matrix A.Consider the following two statements :Statement 1 : eλis an eigen value of eA.Statement 2 : v is an eigen-vector of eA.Which one of the following options is correct?a)Statement 1 is true and statement 2 is false.b)Statement 1 is false and statement 2 is true.c)Both the statements are correct.d)Both the statements are false.Correct answer is option 'C'. Can you explain this answer?
Question Description
eAdenotes the exponential of a square matrix A. Suppose λ is an eigen value and v is the corresponding eigen-vector of matrix A.Consider the following two statements :Statement 1 : eλis an eigen value of eA.Statement 2 : v is an eigen-vector of eA.Which one of the following options is correct?a)Statement 1 is true and statement 2 is false.b)Statement 1 is false and statement 2 is true.c)Both the statements are correct.d)Both the statements are false.Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about eAdenotes the exponential of a square matrix A. Suppose λ is an eigen value and v is the corresponding eigen-vector of matrix A.Consider the following two statements :Statement 1 : eλis an eigen value of eA.Statement 2 : v is an eigen-vector of eA.Which one of the following options is correct?a)Statement 1 is true and statement 2 is false.b)Statement 1 is false and statement 2 is true.c)Both the statements are correct.d)Both the statements are false.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for eAdenotes the exponential of a square matrix A. Suppose λ is an eigen value and v is the corresponding eigen-vector of matrix A.Consider the following two statements :Statement 1 : eλis an eigen value of eA.Statement 2 : v is an eigen-vector of eA.Which one of the following options is correct?a)Statement 1 is true and statement 2 is false.b)Statement 1 is false and statement 2 is true.c)Both the statements are correct.d)Both the statements are false.Correct answer is option 'C'. Can you explain this answer?.
eAdenotes the exponential of a square matrix A. Suppose λ is an eigen value and v is the corresponding eigen-vector of matrix A.Consider the following two statements :Statement 1 : eλis an eigen value of eA.Statement 2 : v is an eigen-vector of eA.Which one of the following options is correct?a)Statement 1 is true and statement 2 is false.b)Statement 1 is false and statement 2 is true.c)Both the statements are correct.d)Both the statements are false.Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about eAdenotes the exponential of a square matrix A. Suppose λ is an eigen value and v is the corresponding eigen-vector of matrix A.Consider the following two statements :Statement 1 : eλis an eigen value of eA.Statement 2 : v is an eigen-vector of eA.Which one of the following options is correct?a)Statement 1 is true and statement 2 is false.b)Statement 1 is false and statement 2 is true.c)Both the statements are correct.d)Both the statements are false.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for eAdenotes the exponential of a square matrix A. Suppose λ is an eigen value and v is the corresponding eigen-vector of matrix A.Consider the following two statements :Statement 1 : eλis an eigen value of eA.Statement 2 : v is an eigen-vector of eA.Which one of the following options is correct?a)Statement 1 is true and statement 2 is false.b)Statement 1 is false and statement 2 is true.c)Both the statements are correct.d)Both the statements are false.Correct answer is option 'C'. Can you explain this answer?.
Solutions for eAdenotes the exponential of a square matrix A. Suppose λ is an eigen value and v is the corresponding eigen-vector of matrix A.Consider the following two statements :Statement 1 : eλis an eigen value of eA.Statement 2 : v is an eigen-vector of eA.Which one of the following options is correct?a)Statement 1 is true and statement 2 is false.b)Statement 1 is false and statement 2 is true.c)Both the statements are correct.d)Both the statements are false.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of eAdenotes the exponential of a square matrix A. Suppose λ is an eigen value and v is the corresponding eigen-vector of matrix A.Consider the following two statements :Statement 1 : eλis an eigen value of eA.Statement 2 : v is an eigen-vector of eA.Which one of the following options is correct?a)Statement 1 is true and statement 2 is false.b)Statement 1 is false and statement 2 is true.c)Both the statements are correct.d)Both the statements are false.Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
eAdenotes the exponential of a square matrix A. Suppose λ is an eigen value and v is the corresponding eigen-vector of matrix A.Consider the following two statements :Statement 1 : eλis an eigen value of eA.Statement 2 : v is an eigen-vector of eA.Which one of the following options is correct?a)Statement 1 is true and statement 2 is false.b)Statement 1 is false and statement 2 is true.c)Both the statements are correct.d)Both the statements are false.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for eAdenotes the exponential of a square matrix A. Suppose λ is an eigen value and v is the corresponding eigen-vector of matrix A.Consider the following two statements :Statement 1 : eλis an eigen value of eA.Statement 2 : v is an eigen-vector of eA.Which one of the following options is correct?a)Statement 1 is true and statement 2 is false.b)Statement 1 is false and statement 2 is true.c)Both the statements are correct.d)Both the statements are false.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of eAdenotes the exponential of a square matrix A. Suppose λ is an eigen value and v is the corresponding eigen-vector of matrix A.Consider the following two statements :Statement 1 : eλis an eigen value of eA.Statement 2 : v is an eigen-vector of eA.Which one of the following options is correct?a)Statement 1 is true and statement 2 is false.b)Statement 1 is false and statement 2 is true.c)Both the statements are correct.d)Both the statements are false.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice eAdenotes the exponential of a square matrix A. Suppose λ is an eigen value and v is the corresponding eigen-vector of matrix A.Consider the following two statements :Statement 1 : eλis an eigen value of eA.Statement 2 : v is an eigen-vector of eA.Which one of the following options is correct?a)Statement 1 is true and statement 2 is false.b)Statement 1 is false and statement 2 is true.c)Both the statements are correct.d)Both the statements are false.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
|
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup