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Consider the system of equation A(nxn)X(nx1) = λ nx1 where, λ is a scalar. Let, (λi, xi) be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correct
- a)For a homogeneous n x n system of linear equations (A - λI)X = 0 having a non - trivial solution when the rank of (A - λI) is less than n
- b)For matrix Am, m being a positive integer, (λim xmi) will be the eigen pair for all i.
- c)If AT = A-1, then |λi | = 1 for all i
- d)If AT = A, then λi is real for all i
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Consider the system of equation A(nxn)X(nx1) = λ nx1where,&lamb...
In order to solve the system of equations A(nxn)X(nx1) = 0, we need to find the values of X that satisfy the equation.
Since A is an nxn matrix and X is an nx1 matrix, the equation can be rewritten as:
A * X = 0
To solve this system of equations, we can use the concept of matrix inversion. If we can find the inverse of matrix A, we can multiply both sides of the equation by the inverse to isolate X:
A^(-1) * A * X = A^(-1) * 0
X = A^(-1) * 0
Since any matrix multiplied by the zero matrix will result in the zero matrix, the solution to the system of equations is:
X = 0
This means that the only solution to the system is X = 0, where all the elements of X are equal to zero.
Since A is an nxn matrix and X is an nx1 matrix, the equation can be rewritten as:
A * X = 0
To solve this system of equations, we can use the concept of matrix inversion. If we can find the inverse of matrix A, we can multiply both sides of the equation by the inverse to isolate X:
A^(-1) * A * X = A^(-1) * 0
X = A^(-1) * 0
Since any matrix multiplied by the zero matrix will result in the zero matrix, the solution to the system of equations is:
X = 0
This means that the only solution to the system is X = 0, where all the elements of X are equal to zero.
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Consider the system of equation A(nxn)X(nx1) = λ nx1where,λ is a scalar. Let, (λi, xi)be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correcta)For a homogeneous n x n system of linear equations (A - λI)X = 0 having a non - trivial solution when the rank of (A - λI) is less than nb)For matrix Am, m being a positive integer, (λimxmi) will be the eigen pair for all i.c)If AT = A-1, then |λi | = 1 for all id)If AT = A, then λi is real for all iCorrect answer is option 'B'. Can you explain this answer?
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Consider the system of equation A(nxn)X(nx1) = λ nx1where,λ is a scalar. Let, (λi, xi)be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correcta)For a homogeneous n x n system of linear equations (A - λI)X = 0 having a non - trivial solution when the rank of (A - λI) is less than nb)For matrix Am, m being a positive integer, (λimxmi) will be the eigen pair for all i.c)If AT = A-1, then |λi | = 1 for all id)If AT = A, then λi is real for all iCorrect answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Consider the system of equation A(nxn)X(nx1) = λ nx1where,λ is a scalar. Let, (λi, xi)be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correcta)For a homogeneous n x n system of linear equations (A - λI)X = 0 having a non - trivial solution when the rank of (A - λI) is less than nb)For matrix Am, m being a positive integer, (λimxmi) will be the eigen pair for all i.c)If AT = A-1, then |λi | = 1 for all id)If AT = A, then λi is real for all iCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the system of equation A(nxn)X(nx1) = λ nx1where,λ is a scalar. Let, (λi, xi)be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correcta)For a homogeneous n x n system of linear equations (A - λI)X = 0 having a non - trivial solution when the rank of (A - λI) is less than nb)For matrix Am, m being a positive integer, (λimxmi) will be the eigen pair for all i.c)If AT = A-1, then |λi | = 1 for all id)If AT = A, then λi is real for all iCorrect answer is option 'B'. Can you explain this answer?.
Consider the system of equation A(nxn)X(nx1) = λ nx1where,λ is a scalar. Let, (λi, xi)be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correcta)For a homogeneous n x n system of linear equations (A - λI)X = 0 having a non - trivial solution when the rank of (A - λI) is less than nb)For matrix Am, m being a positive integer, (λimxmi) will be the eigen pair for all i.c)If AT = A-1, then |λi | = 1 for all id)If AT = A, then λi is real for all iCorrect answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Consider the system of equation A(nxn)X(nx1) = λ nx1where,λ is a scalar. Let, (λi, xi)be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correcta)For a homogeneous n x n system of linear equations (A - λI)X = 0 having a non - trivial solution when the rank of (A - λI) is less than nb)For matrix Am, m being a positive integer, (λimxmi) will be the eigen pair for all i.c)If AT = A-1, then |λi | = 1 for all id)If AT = A, then λi is real for all iCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the system of equation A(nxn)X(nx1) = λ nx1where,λ is a scalar. Let, (λi, xi)be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correcta)For a homogeneous n x n system of linear equations (A - λI)X = 0 having a non - trivial solution when the rank of (A - λI) is less than nb)For matrix Am, m being a positive integer, (λimxmi) will be the eigen pair for all i.c)If AT = A-1, then |λi | = 1 for all id)If AT = A, then λi is real for all iCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Consider the system of equation A(nxn)X(nx1) = λ nx1where,λ is a scalar. Let, (λi, xi)be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correcta)For a homogeneous n x n system of linear equations (A - λI)X = 0 having a non - trivial solution when the rank of (A - λI) is less than nb)For matrix Am, m being a positive integer, (λimxmi) will be the eigen pair for all i.c)If AT = A-1, then |λi | = 1 for all id)If AT = A, then λi is real for all iCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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Consider the system of equation A(nxn)X(nx1) = λ nx1where,λ is a scalar. Let, (λi, xi)be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correcta)For a homogeneous n x n system of linear equations (A - λI)X = 0 having a non - trivial solution when the rank of (A - λI) is less than nb)For matrix Am, m being a positive integer, (λimxmi) will be the eigen pair for all i.c)If AT = A-1, then |λi | = 1 for all id)If AT = A, then λi is real for all iCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Consider the system of equation A(nxn)X(nx1) = λ nx1where,λ is a scalar. Let, (λi, xi)be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correcta)For a homogeneous n x n system of linear equations (A - λI)X = 0 having a non - trivial solution when the rank of (A - λI) is less than nb)For matrix Am, m being a positive integer, (λimxmi) will be the eigen pair for all i.c)If AT = A-1, then |λi | = 1 for all id)If AT = A, then λi is real for all iCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Consider the system of equation A(nxn)X(nx1) = λ nx1where,λ is a scalar. Let, (λi, xi)be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correcta)For a homogeneous n x n system of linear equations (A - λI)X = 0 having a non - trivial solution when the rank of (A - λI) is less than nb)For matrix Am, m being a positive integer, (λimxmi) will be the eigen pair for all i.c)If AT = A-1, then |λi | = 1 for all id)If AT = A, then λi is real for all iCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the system of equation A(nxn)X(nx1) = λ nx1where,λ is a scalar. Let, (λi, xi)be an eigen pair of an eigen value and its corresponding eigen vector for real matrix A. Let I be a (n x n) unit matrix. Which one of the following statements is not correcta)For a homogeneous n x n system of linear equations (A - λI)X = 0 having a non - trivial solution when the rank of (A - λI) is less than nb)For matrix Am, m being a positive integer, (λimxmi) will be the eigen pair for all i.c)If AT = A-1, then |λi | = 1 for all id)If AT = A, then λi is real for all iCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Mathematics tests.
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