1. Find LU Decomposition using Gauss Elimination method of Matrix ...
`[[8,-6,2],[-6,7,-4],[2,-4,3]]`

Solution:

Here `A`

=

`8` `-6` `2` `-6` `7` `-4` `2` `-4` `3`

Using Gaussian Elimination method
`R_2 larr R_2-``(-0.75)``xx R_1` `[:.L_(2,1)=color{blue}{-0.75}]`

=	`8` `-6` `2` `0` `2.5` `-2.5` `2` `-4` `3`

`R_3 larr R_3-``(0.25)``xx R_1` `[:.L_(3,1)=color{blue}{0.25}]`

=	`8` `-6` `2` `0` `2.5` `-2.5` `0` `-2.5` `2.5`

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

=	`8` `-6` `2` `0` `2.5` `-2.5` `0` `0` `0`

`:.U`

=

`8` `-6` `2` `0` `2.5` `-2.5` `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}{-0.75}` `1` `0` `color{blue}{0.25}` `color{blue}{-1}` `1`

Now checking `A=LU` ?

`LU`

=

`1` `0` `0` `-0.75` `1` `0` `0.25` `-1` `1`

`xx`

`8` `-6` `2` `0` `2.5` `-2.5` `0` `0` `0`

=

`8` `-6` `2` `-6` `7` `-4` `2` `-4` `3`

And `A`

=

`8` `-6` `2` `-6` `7` `-4` `2` `-4` `3`

Solution is possible.

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