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## Homework Statement

Suppose that AB = 0, where A is a 3 x 7 full rank matrix and B is 7 x 53. What is the highest possible rank of matrix B.

## Homework Equations

## The Attempt at a Solution

Since each column of B is in the null space of A, the rank of B is at most 4.

I don't understand why it is 4.

What operation do I need to perform here to understand this? I am not a student, I am just trying to remember Linear Algebra.