題組內容

4. Given the following linear system:

$$\left\{ \begin{array}{l} x1 + 4x2 + 3x3 = 2 \\ -x1 - 2x2 = -3 \\ 2x1 + 2x2 + 3x3 = 1 \end{array} \right.$$

The above linear system can be expressed as the matrix representation $A\vec{x} = \vec{b}$.

(b) (5%) (Triangular Factorization problem) Let \( A = LU \), where \( L \) and \( U \) denote the lower triangular matrix and upper triangular matrix, respectively. Find \( L \).