[Solution] Consider the following matrix.


Question: Consider the following matrix.

\[A=\left[\begin{array}{ccc} 2 & 1 & -3 \\ 0 & 2 & 2 \\ 0 & -1 & -1 \\ -1 & -3 & -1 \\ 1 & 2 & 0 \end{array}\right]\]
  1. What is the column space of \(A\) ?
  2. Find the left null space of \(A\).
  3. Compare the dimensions of the column space and left null space.

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