+1 vote
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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. $6$

edited | 145 views
check the lectures from Khan's academy on LU decomposition . Its nice and short.
Can you give a link if you have it? I was unable to find it.

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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