If the rank of A=((A_(11),A_(21)),(A_(12),A_(22)) is 2, we must have A_(11) != 0 or A_(21) != 0. I understand that this is because A must have two linearly independent columns/rows , but why doesn't it say that A_(12) != 0 or A_(22) != 0?

themediamafia73 2022-09-11 Answered
If the rank of
A = ( A 11 A 12 A 21 A 22 )
is 2, we must have A 11 0 or A 21 0. I understand that this is because A must have two linearly independent columns/rows , but why doesn't it say that A 12 0 or A 22 0?
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Answers (1)

Makhi Adams
Answered 2022-09-12 Author has 13 answers
If either A 11 = A 21 = 0 or A 12 = A 22 = 0, then the rank is less than 2 (Note that this is not an if and only if).
Both are true, and they decided to mention only the former.
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