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Problem: lu decomposition [[8,-6,2],[-6,7,-4],[2,-4,3]] [ Calculator, Method and examples ]

Solution:
Your problem -> lu decomposition [[8,-6,2],[-6,7,-4],[2,-4,3]]

LU decomposition : If we have a matrix A, then an upper triangular matrix U can be obtained without pivoting under Gaussian Elimination method, and there exists lower triangular matrix L such that A=LU.

Here A =
 8 -6 2 -6 7 -4 2 -4 3

Using Gaussian Elimination method
R_2 larr R_2-(-3/4)xx R_1 [:.L_(2,1)=color{blue}{-3/4}]

=
 8 -6 2 0 5/2 -5/2 2 -4 3

R_3 larr R_3-(1/4)xx R_1 [:.L_(3,1)=color{blue}{1/4}]

=
 8 -6 2 0 5/2 -5/2 0 -5/2 5/2

R_3 larr R_3-(-1)xx R_2 [:.L_(3,2)=color{blue}{-1}]

=
 8 -6 2 0 5/2 -5/2 0 0 0

:.U =
 8 -6 2 0 5/2 -5/2 0 0 0

L is just made up of the multipliers we used in Gaussian elimination with 1s on the diagonal.

:.L =
 1 0 0 color{blue}{-3/4} 1 0 color{blue}{1/4} color{blue}{-1} 1

:. LU decomposition for A is

A =
 8 -6 2 -6 7 -4 2 -4 3
=
 1 0 0 -3/4 1 0 1/4 -1 1
xx
 8 -6 2 0 5/2 -5/2 0 0 0
= LU

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