5. Find the rank and nullity of the linear transformation $$ T: R^{3} \rightarrow R^{3} $$ defined by $$ A=\left(\begin{array}{ccc}1 & 0 & -2 \ 0 & 1 & 1 \ 0 & 0 & 0\end{array}\right) $$

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The transformation $$ A $$ has a rank of 2 and a nullity of 1.

5. Find the rank and nullity of the linear transformation \( T: R^{3} \rightarrow R^{3} \) defined by \[ A=\left(\begin{array}{ccc}1 & 0 & -2 \\ 0 & 1 & 1 \\ 0 & 0 & 0\end{array}\right) \]

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5. Find the rank and nullity of the linear transformation \( T: R^{3} \rightarrow R^{3} \) defined by \[ A=\left(\begin{array}{ccc}1 & 0 & -2 \\ 0 & 1 & 1 \\ 0 & 0 & 0\end{array}\right) \]

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