Question:
If A is a 3 by 5 matrix, what information do you have about the nullspace of A?
Answer:
N(A) has dimension at least 2 and at most 5.
My trouble:
How do we know this?

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m>=r
m=3 so 0=

You're using the notation where m is the number of rows and r is the rank, right?

yes
m=#rows
n=#columns
r=rank

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