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If A is a non-zero column matrix of order m x1 and B is a non-zero row matrix of order 1 x n, then rank of AB is equal to
  • a)
    m
  • b)
    n
  • c)
    1
  • d)
    none of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If A is a non-zero column matrix of order m x1 and B is a non-zero row...
Let
be two non-zero column and row matrices respectively
Since A, B are non-zero matrices. .% matrix AB will be a non-zero matrix. The matrix AB will have at least one non-zero element obtained by multiplying corresponding non-zero elements of A and B. All the two rowed minors of AB clearly vanish. Since AB is non-zero matrix,
∴ rank of AB = 1
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Community Answer
If A is a non-zero column matrix of order m x1 and B is a non-zero row...
Let
be two non-zero column and row matrices respectively
Since A, B are non-zero matrices. .% matrix AB will be a non-zero matrix. The matrix AB will have at least one non-zero element obtained by multiplying corresponding non-zero elements of A and B. All the two rowed minors of AB clearly vanish. Since AB is non-zero matrix,
∴ rank of AB = 1
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If A is a non-zero column matrix of order m x1 and B is a non-zero row matrix of order 1 x n, then rank of AB is equal toa)mb)nc)1d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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If A is a non-zero column matrix of order m x1 and B is a non-zero row matrix of order 1 x n, then rank of AB is equal toa)mb)nc)1d)none of theseCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If A is a non-zero column matrix of order m x1 and B is a non-zero row matrix of order 1 x n, then rank of AB is equal toa)mb)nc)1d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A is a non-zero column matrix of order m x1 and B is a non-zero row matrix of order 1 x n, then rank of AB is equal toa)mb)nc)1d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
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