LU decomposition using Crout's method of matrix Example [[2,3],[4,10]]

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Home > Matrix & Vector > Matrix operation > LU decomposition using Crout's method of Matrix example

10. LU decomposition using Crout's method of matrix example ( Enter your problem )

( Enter your problem )

4. Example `[[2,3],[4,10]]`

Find LU decomposition using Crout's method of Matrix ...
`[[2,3],[4,10]]`

Solution:
Crout's method for LU decomposition
Let `A=LU`

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

	`l_(11)`	`0`
	`l_(21)`	`l_(22)`

`xx`

	`1`	`u_(12)`
	`0`	`1`

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

	`l_(11)`	`l_(11)u_(12)`
	`l_(21)`	`l_(21)u_(12) + l_(22)`

This implies
`l_(11)=2`

`l_(11)u_(12)=3=>2xxu_(12)=3=>u_(12)=1.5`

`l_(21)=4`

`l_(21)u_(12) + l_(22)=10=>4xx1.5 + l_(22)=10=>l_(22)=4`

Now checking `A=LU` ?

`LU`

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

`xx`

	`1`	`1.5`
	`0`	`1`

	`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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