Given the following matrix \(A\) and its rref, find bases fo…
Given the following matrix \(A\) and its rref, find bases for \(\text{row}\left(A\right), \text{col}\left(A\right),\) and \(\text{null}\left(A\right)\). Also, state the rank and nullity of \(A\). \[A=\begin{bmatrix}1&3&2&7&1&-1&3\\3&9&1&17&-3&-12&-3\\-1&-3&0&-5&1&-21&1\\-1&-3&5&5&4&0&7\end{bmatrix}\] \[\text{rref}\left(A\right)=\begin{bmatrix}1&3&0&5&0&1&1\\0&0&1&2&0&-3&0\\0&0&0&0&1&4&2\\0&0&0&0&0&0&0\end{bmatrix}\]
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