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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?
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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.
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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.
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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?
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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).
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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.
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