Problem

Find the LU Decomposition of the matrix \( A = \begin{bmatrix} 4 & 3 \newline 6 & 3 \end{bmatrix} \)

Solution

Step 1 :Step 1: Initialize the identity matrix \( I = \begin{bmatrix} 1 & 0 \newline 0 & 1 \end{bmatrix} \) and the matrix \( L = I \)

Step 2 :Step 2: Perform row operations to convert \( A \) into an upper triangular matrix \( U \). Multiply row 2 by \( \frac{4}{6} \) and subtract row 1 from it. Now, \( U = \begin{bmatrix} 4 & 3 \newline 0 & -1 \end{bmatrix} \)

Step 3 :Step 3: Inverse the operations performed on \( A \) to get \( L \). Divide row 2 by \( \frac{4}{6} \) and add row 1 to it. Now, \( L = \begin{bmatrix} 1 & 0 \newline \frac{3}{2} & 1 \end{bmatrix} \)

From Solvely APP
Source: https://solvelyapp.com/problems/VpqwDcp3bv/

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