LU decomposition using Gauss Elimination method of matrix Example [[2,3],[4,10]]

Find LU Decomposition using Gauss Elimination method of Matrix ...
`[[2,3],[4,10]]`

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`

	`2`	`3`
	`4`	`10`

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

	`2`	`3`
	`0`	`4`

`:.U`

	`2`	`3`
	`0`	`4`

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

`:.L`

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

Now checking `A=LU` ?

`LU`

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

`xx`

	`2`	`3`
	`0`	`4`

	`2`	`3`
	`4`	`10`

And `A`

	`2`	`3`
	`4`	`10`

Solution is possible.

This material is intended as a summary. Use your textbook for detail explanation.
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4. Example `[[2,3],[4,10]]`