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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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