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

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Home > Matrix & Vector calculators > LU Decomposition using Gauss Elimination method of Matrix example

8. LU decomposition using Gauss Elimination method of matrix example ( Enter your problem )

( Enter your problem )

3. Example

[111-1-3-3244] $[[1,1,1],[-1,-3,-3],[2,4,4]]$
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9. LU decomposition using Doolittle's method of matrix
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4. Example [23410] $[[2,3],[4,10]]$

Find LU Decomposition using Gauss Elimination method of Matrix ...
[23410] $[[2,3],[4,10]]$

Solution:

LU $LU$ 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 $A$

	2 $2$	3 $3$
	4 $4$	10 $10$

Using Gaussian Elimination method

R2←R2- $R_2 larr R_2-$

(2) $(2)$

×R1 $xx R_1$

[∴L2,1=2] $[:.L_(2,1)=color{blue}{2}]$

	2 $2$	3 $3$
	0 $0$	4 $4$

∴U $:.U$

	2 $2$	3 $3$
	0 $0$	4 $4$

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

∴L $:.L$

	1 $1$	0 $0$
	2 $color{blue}{2}$	1 $1$

∴ $:.$ LU decomposition for A is

A $A$

	2 $2$	3 $3$
	4 $4$	10 $10$

	1 $1$	0 $0$
	2 $2$	1 $1$

× $xx$

	2 $2$	3 $3$
	0 $0$	4 $4$

LU $LU$

This material is intended as a summary. Use your textbook for detail explanation.
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