in Linear Algebra edited by
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$\begin{pmatrix}
4&3 \\
6&3 
\end{pmatrix}$

What is the sum of all the elements of the $L$ and $U$ matrices as obtained in the L U decomposition?

  1. $16$
  2. $10$
  3. $9$
  4. $6$

in Linear Algebra edited by
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check the lectures from Khan's academy on LU decomposition . Its nice and short.
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Can you give a link if you have it? I was unable to find it.
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4 Answers

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Answer is 9

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

and then equals to main matrix and find corresponding values
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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