LU decomposition using Gauss Elimination method of matrix Example [[1,1,1],[-1,-3,-3],[2,4,4]]

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

Solution:

`LU` decomposition : If we have a square 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`

`1`	`1`	`1`
`-1`	`-3`	`-3`
`2`	`4`	`4`

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

`1`	`1`	`1`
`0`	`-2`	`-2`
`2`	`4`	`4`

`R_3 larr R_3-``(2)``xx R_1` `[:.L_(3,1)=color{blue}{2}]`

`1`	`1`	`1`
`0`	`-2`	`-2`
`0`	`2`	`2`

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

`1`	`1`	`1`
`0`	`-2`	`-2`
`0`	`0`	`0`

`:.U`

`1`	`1`	`1`
`0`	`-2`	`-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}{-1}`	`1`	`0`
`color{blue}{2}`	`color{blue}{-1}`	`1`

Now checking `A=LU` ?

`LU`

`1`	`0`	`0`
`-1`	`1`	`0`
`2`	`-1`	`1`

`xx`

`1`	`1`	`1`
`0`	`-2`	`-2`
`0`	`0`	`0`

`1`	`1`	`1`
`-1`	`-3`	`-3`
`2`	`4`	`4`

And `A`

`1`	`1`	`1`
`-1`	`-3`	`-3`
`2`	`4`	`4`

Solution is possible.

This material is intended as a summary. Use your textbook for detail explanation.
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3. Example `[[1,1,1],[-1,-3,-3],[2,4,4]]`