Exercise6

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

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

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

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

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

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

in-context