in Linear Algebra edited by
1,486 views
7 votes
7 votes
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$?$
in Linear Algebra edited by
1.5k views

1 Answer

6 votes
6 votes
Best answer
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
selected by

4 Comments

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.
0
0

if the diagonal elements of Uare both 1

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

0
0
Here clearly say Upper triangular matrix U have both diagonals $1$,so we can apply Crout's method
0
0

Related questions