check the lectures from Khan's academy on LU decomposition . Its nice and short.

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1 vote

$\begin{bmatrix} 4 & 3\\ 6 & 3 \end{bmatrix} = \begin{bmatrix} l11 & 0\\ l21 & l22 \end{bmatrix}\begin{bmatrix} u11 & u12\\ 0 & u22 \end{bmatrix} \\ \\ \text{We get following equations :} \\l11*u11 + 0*0 = 4 \\l11*u12 + 0*u22 = 3 \\l21*u11 + l22*0 = 6 \\l21*u12 + l22*u22 = 3 \\ \\ \text{After solving above equations, we get,} \\ l21 = 1.5 \\ u11 = 4 \\ u12 = 3 \\ u22 = -1.5 \\ \\ \text{Substitute this value in above LU decomposed materix, we get} \\ \begin{bmatrix} 4 & 3\\ 6 & 3 \end{bmatrix} = \begin{bmatrix} 1 & 0\\ 1.5 & 1 \end{bmatrix}\begin{bmatrix} 4 & 3\\ 0 & -1.5 \end{bmatrix} \\ \\ \text{Summing all the values in LU matrix, we get sum = 9}$

0 votes

Matrix A= LU

For L(lower triangular), all elements above the diagonal will be zero. All diagonal elements will be 1. Take the Matrix A, use row operations and convert elements above the diagonal as 0. Then using L and Matrix A, solve U. See this--> https://gateoverflow.in/?qa=blob&qa_blobid=9819239900743812923