2. (10%) Let \( A = \begin{bmatrix} 2 & 1 & 1 \\ 6 & 4 & 5 \\ 4 & 1 & 3 \end{bmatrix} \). Find an upper triangular matrix \( U \) and a lower triangular matrix \( L \) such that \( A = LU \).
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2. (10%) Let \( A = \begin{bmatrix} 2 & 1 & 1 \\ 6 & 4 & 5 \\ 4 & 1 & 3 \end{bmatrix} \). Find an upper triangular matrix \( U \) and a lower triangular matrix \( L \) such that \( A = LU \).