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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'

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+1 vote
d because there is no determinent of size greate than equal r to whose det is not zero
by (71 points)

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.

by Active (1.5k points)