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In the LU decomposition of the matrix,$\begin{bmatrix} 1 &2 \\ 3 &8 \end{bmatrix}$ if the diagonal elements of $U$ are both $1$, then the trace of $L$ is$?$

Since, A=LU

$\begin{bmatrix} 1 &2 \\ 3&8 \end{bmatrix}$ = $\begin{bmatrix} l1 &0 \\ l2&l3 \end{bmatrix}$ $\begin{bmatrix} 1 &u1 \\ 0&1 \end{bmatrix}$

= $\begin{bmatrix} l1 &l1 u1 \\l2&l2u1+l3 \end{bmatrix}$

Solving this,

$l1$ =1

$l3$ =2

So,  trace(L)= $l1$ + $l3$ = 3

moved
This is crout LU Decomposition.

Lakshman Patel RJIT

But in LU decompostion we consider ..diagonal elements as 1 in Lower triangular matrix right ??

see this

Pdf taken from Gatecse resources

can you send me pdf link?
if the diagonal elements of $U$ are both $1,$

So we can apply Crout's Method.

and you provide me pdf which is used Gaussian elimination method.

if the diagonal elements of Uare both 1

If this line is not mentioned just LU decomposition mentioned then wht we should take ?

Here clearly say Upper triangular matrix U have both diagonals $1$,so we can apply Crout's method

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