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Solution of linear systems

How to use the different techniques to solve linear systems? A discussion of Lower upper factorization is presented with full detailed solved problems for 2×2 matrices and 3×3 matrices.

6- Easy introduction to permutation matrix

August 13, 2026February 7, 2024 by Maged kamel
An introduction to permutation matrix

The post includes an introduction to permutation matrix for both 2×2 and 3×3 matrices. How to change the arrangement of rows and columns for matrices?

Categories Solution of linear systems Tags Introduction to Permutation matrix.

5c- Solved problem for x-y-z values by LU decomposition.

August 13, 2026February 3, 2024 by Maged kamel
Solved problem for x-y-z values by LU decomposition.

The solved problem for x-y-z values by using the LU decomposition. for three simultaneous equations. Step by step illustration is explained.

Categories Solution of linear systems Tags Solved problem for x-y-z values by LU decomposition

5b-Find the three unknowns for the second solved problem

August 13, 2026February 2, 2024 by Maged kamel
The content of post 5b-numerical linear.

Find the three unknowns for the Second solved problem. Two method to be used to solve for x1, x2 and x3.

Categories Solution of linear systems Tags Find the three unknowns for the second solved problem

5A- Second solved problem-LU decomposition-3×3 matrix

August 13, 2026January 20, 2021 by Maged kamel
Second solved problem-LU decomposition-3×3 matrix-part 1-Find L and U.

The second solved problem-LU decomposition for the 3×3 matrices, how to get x,y,z values for three simultaneous equations?

Categories Solution of linear systems Tags A second Solved problem for LU for 3x3 matrix.

5- First solved problem: LU decomposition for the 3×3 matrix

August 13, 2026January 15, 2021 by Maged kamel
First solved problem-LU decomposition for the 3x3 matrix.

This post illustrates the first solved problem-LU decomposition for the 3×3 matrix. Step by step guide to solve 3 simultaneous equations by the LU method?

Categories Solution of linear systems Tags Solved problems for LU decomposition for 3x3 matrix.

4-Derive the expression for L-U values for a 3×3 matrix.

August 13, 2026January 1, 2021 by Maged kamel
Brief illustration of Post 4- numerical linear.

Step-by-step guide on how to derive the expression for L-U values for-3×3 matrix using Doolittle’s method?

Categories Solution of linear systems Tags How to derive the expression for L-U values for-3x3 matrix?

3-How to solve for x-y by L-U Decomposition?

August 13, 2026December 20, 2020 by Maged kamel
How to solve for x-y by L-U Decomposition?

How to solve for x-y by L-U Decomposition? Illustration by Gauss elimination for L and U matrices.

Categories Solution of linear systems Tags Solving for the x and y for two equations by L/U Decomposition

2- Easy illustration of LU decomposition for a 2×2 matrix

August 13, 2026December 14, 2020 by Maged kamel
Easy illustration for LU decomposition for 2×2 matrix.

How to use the Lu decomposition method for a 2×2 matrix? A step-by-step guide to find L and U values?

Categories Solution of linear systems Tags How to find the L/U decomposition for the 2x2 matrix-Doolittle's method?, Video How to convert A matrix to L*U
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