###### Exercise 6

Suppose that \(A\) is a \(3\times 4\) matrix.

Is it possible that \(\dim~\nul(A) = 0\text{?}\)

If \(\dim~\nul(A) = 1\text{,}\) what can you say about \(\col(A)\text{?}\)

If \(\dim~\nul(A) = 2\text{,}\) what can you say about \(\col(A)\text{?}\)

If \(\dim~\nul(A) = 3\text{,}\) what can you say about \(\col(A)\text{?}\)

If \(\dim~\nul(A) = 4\text{,}\) what can you say about \(\col(A)\text{?}\)