Let \( A=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1\end...

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Let \( A=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1\end{array}\right] \). If \( U_{1} \) and \( U_{2} \) are column matrices such that \( A U_{1}=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right] \) and \( A U_{2}=\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right] \), then find \( U_{1}+U_{2} \).
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