GATE Papers >> CSE >> 2015 >> Question No 33

Question No. 33 CSE | GATE 2015

In the LU decomposition of the matrix 2249,if the diagonal elements of $U$ are both 1, then the lower diagonal entry $l_{22}$ of $L$ is ______.


Answer : 5


Solution of Question No 33 of GATE 2015 CSE Paper

$ \begin{bmatrix}L_{11}&0\\L_{21}&L_{22}\end{bmatrix}\begin{bmatrix}1&U_{12}\\0&1\end{bmatrix}=\begin{bmatrix}2&2\\4&9\end{bmatrix} $

This is crout's LU decomposition, since diagonal elements of U are 1. So we will setup the equations for the elements of the matrix taken column-wise, as follows

$ \begin{array}{l}\;\;\;\;\;L_{11}=2,\;L_{21}=4\\\;\;\;\;\;\;\;\;\;\;L_{11}\times U_{12}=2\\\Rightarrow\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;U_{12}=1,\\L_{21}\times U_{12}+L_{22}=9\\\Rightarrow\;\;\;\;\;\;\;\;4+{\mathrm L}_{22}=9\\\Rightarrow\;\;\;\;\;\;\;\;\;\;\;\;\;\;L_{22}=5\end{array} $

Comments
qySuAk http://pills2sale.com/ levitra nizagara

Posted on  18/10/2020 18:23:48  by  dobsonz
KUghTR http://pills2sale.com/ levitra nizagara

Posted on  18/10/2020 21:18:51  by  dobsonz
XSigYZ http://pills2sale.com/ viagra cialis buy

Posted on  01/11/2020 20:18:13  by  johnanx
Leave a comment
Go