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+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. $6$

 

 

asked in Linear Algebra by Active (1.5k points)  
edited by | 125 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.

4 Answers

+2 votes
Best answer

Answer is 9

answered by Veteran (19.2k points)  
selected by
+1 vote
$\begin{bmatrix} 4 & 3\\ 6 & 3 \end{bmatrix} = \begin{bmatrix} l11 & 0\\ l21 & l22 \end{bmatrix}\begin{bmatrix} u11 & u12\\ 0 & u22 \end{bmatrix} \\ \\ \text{We get following equations :} \\l11*u11 + 0*0 = 4 \\l11*u12 + 0*u22 = 3 \\l21*u11 + l22*0 = 6 \\l21*u12 + l22*u22 = 3 \\ \\ \text{After solving above equations, we get,} \\ l21 = 1.5 \\ u11 = 4 \\ u12 = 3 \\ u22 = -1.5 \\ \\ \text{Substitute this value in above LU decomposed materix, we get} \\ \begin{bmatrix} 4 & 3\\ 6 & 3 \end{bmatrix} = \begin{bmatrix} 1 & 0\\ 1.5 & 1 \end{bmatrix}\begin{bmatrix} 4 & 3\\ 0 & -1.5 \end{bmatrix} \\ \\ \text{Summing all the values in LU matrix, we get sum = 9}$
answered by Active (1.5k points)  
edited by
0 votes
divison into lower triangulatr and uppertriangular

and then equals to main matrix and find corresponding values
answered by Junior (679 points)  
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--> http://gateoverflow.in/?qa=blob&qa_blobid=9819239900743812923

answered by Loyal (3.3k points)  
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