Exercise2

Suppose that

\begin{equation*} A = \left[\begin{array}{rrrr} 2 \amp 0 \amp -2 \amp -4 \\ -2 \amp -1 \amp 1 \amp 2 \\ 0 \amp -1 \amp -1 \amp -2 \end{array}\right] \text{.} \end{equation*}
  1. Is the vector \(\threevec{0}{-1}{-1}\) in \(\col(A)\text{?}\)

  2. Is the vector \(\fourvec{2}{1}{0}{2}\) in \(\col(A)\text{?}\)

  3. Is the vector \(\threevec{2}{-2}{0}\) in \(\nul(A)\text{?}\)

  4. Is the vector \(\fourvec{1}{-1}{3}{-1}\) in \(\nul(A)\text{?}\)

  5. Is the vector \(\fourvec{1}{0}{1}{-1}\) in \(\nul(A)\text{?}\)

in-context