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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

December 17, 2025February 7, 2023 by Maged kamel
An introduction to permutation matrix

The post includes an introduction to the 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.

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

December 17, 2025November 14, 2022 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

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

December 15, 2025January 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

December 14, 2025January 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-3×3 matrix.

December 15, 2025December 1, 2020 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?

December 15, 2025November 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

1- Easy introduction to the Inverse of a Matrix-2×2 matrix.

December 14, 2025October 15, 2020 by Maged kamel
Easy introduction to Inverse of a Matrix-2x2 matrix.

How to get the inverse of a matrix by creating an identity matrix. A solved example is given for the inverse of a 2×2 matrix.

Categories Solution of linear systems Tags Find the inverse of a 2x2 matrix, Video How can we find the inverse of 2x2 matrix?
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