Solution
= Solution
The first pivot is two. <Gaussian elimination> without <partial pivoting> uses $R_2\leftarrow R_2-2R_1$ and $R_3\leftarrow R_3-4R_1$, giving
$$
\begin{pmatrix}2&1&1\\0&1&1\\0&3&5\end{pmatrix}.
$$
The second pivot is one; $R_3\leftarrow R_3-3R_2$ gives the <upper triangular matrix>
$$
\boxed{U=\begin{pmatrix}2&1&1\\0&1&1\\0&0&2\end{pmatrix}.}
$$
Both pivots used for division are nonzero, so no row exchange is needed.