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If every minor of order 'r' of a matrix 'A' is zero, then rank of 'A' is

a) greater than 'r'
b) equal to 'r'
c) less than or equal to 'r'
d) less than 'r'
in Linear Algebra by
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2 Answers

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d because there is no determinent of size greate than equal r to whose det is not zero
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Given an m × n matrix with real entries (or entries from any other field) and rank r, then there exists at least one non-zero r × r minor, while all larger minors are zero. Hence answer is option D.

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