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If the rank of a (5×6) matrix Q is 4, then which one of the following statements is correct?
- a)Q will have four linearly independent rows and four linearly independent columns
- b)Q will have four lineally independent rows and five lineally independent columns
- c)QQT will be invertible
- d)QTQ will be invertible
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the rank of a (5×6) matrix Q is 4, then which one of the follo...
Given that rank Q is 4, so it will have 4 linearly independent columns as well as 4 linearly independent rows (∵ row rank of a matrix = column rank of a matrix)
So, A is correct and accordingly B is false.
C is false as order of QQ^T will be 5 x 5 and given that rank of Q is 4 i.e. < 5. So the matrix is QQ^T will be singular and hence not invertible.
Similarly D is false as order of Q^T Q will be 6 x 6 and the matrix is Q^T Q will be singular and hence not invertible.
Most Upvoted Answer
If the rank of a (5×6) matrix Q is 4, then which one of the follo...
A row is Linearly Independent if you can't represent that row using other rows( using elementary operations).And if a row is Linearly dependent then you can make that row 0 as it can be represented by using EOs on other rows. So if rank of matrix is 4, it means there will be at max 4 non-zero rows in Row Echleon form and If you can't make anymore rows 0 that means they are Linearly Independent.
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Community Answer
If the rank of a (5×6) matrix Q is 4, then which one of the follo...
In option A the conjunction "and" is used. That's the error only. There should be "or", according to me.
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If the rank of a (5×6) matrix Q is 4, then which one of the following statements is correct? a)Q will have four linearly independent rows and four linearly independent columns b)Q will have four lineally independent rows and five lineally independent columnsc)QQT will be invertibled)QTQ will be invertibleCorrect answer is option 'A'. Can you explain this answer?
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If the rank of a (5×6) matrix Q is 4, then which one of the following statements is correct? a)Q will have four linearly independent rows and four linearly independent columns b)Q will have four lineally independent rows and five lineally independent columnsc)QQT will be invertibled)QTQ will be invertibleCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about If the rank of a (5×6) matrix Q is 4, then which one of the following statements is correct? a)Q will have four linearly independent rows and four linearly independent columns b)Q will have four lineally independent rows and five lineally independent columnsc)QQT will be invertibled)QTQ will be invertibleCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the rank of a (5×6) matrix Q is 4, then which one of the following statements is correct? a)Q will have four linearly independent rows and four linearly independent columns b)Q will have four lineally independent rows and five lineally independent columnsc)QQT will be invertibled)QTQ will be invertibleCorrect answer is option 'A'. Can you explain this answer?.
If the rank of a (5×6) matrix Q is 4, then which one of the following statements is correct? a)Q will have four linearly independent rows and four linearly independent columns b)Q will have four lineally independent rows and five lineally independent columnsc)QQT will be invertibled)QTQ will be invertibleCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about If the rank of a (5×6) matrix Q is 4, then which one of the following statements is correct? a)Q will have four linearly independent rows and four linearly independent columns b)Q will have four lineally independent rows and five lineally independent columnsc)QQT will be invertibled)QTQ will be invertibleCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the rank of a (5×6) matrix Q is 4, then which one of the following statements is correct? a)Q will have four linearly independent rows and four linearly independent columns b)Q will have four lineally independent rows and five lineally independent columnsc)QQT will be invertibled)QTQ will be invertibleCorrect answer is option 'A'. Can you explain this answer?.
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