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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.

10-Solved problems for 3×3 matrix by Crout’s LU-option 1.

September 18, 2025November 1, 2024 by Maged kamel
Two solved problems for The Crout's LU decomposition.

Two solved problems for 3×3 matrix by Crout’s LU decomposition. Option 1 is used for which the matrix is converted to a lower matrix.

Categories Solution of linear systems Tags solved problems for (3x3) matrix by Crout's LU decomposition.

9A- A Second option for Crout’s LU decomposition-3×3 matrix

September 18, 2025October 29, 2024 by Maged kamel
brief illustration post 9 numerical linear

A Second option for Crout’s LU decomposition-3×3 matrix. How to covert the A matrix to an upper matrix? How to get the values of L and U matrices?

Categories Solution of linear systems Tags Second option for Crout's LU decomposition for a 3x3 matrix

9- Crout’s LU decomposition for a 3×3 matrix-Option 1

September 18, 2025April 1, 2024 by Maged kamel
Crout's LU decomposition for a 3x3 matrix-Option 1

How to drive Crout’s LU decomposition for a 3×3 matrix-option-1? Step-by-step introduction to Crout’s LU decomposition for a 3×3 matrix.

Categories Solution of linear systems Tags Crout's LU decomposition for a 3x3 matrix-option 1

8-Introduction to Crout’s LU decomposition for a 2×2 matrix.

September 18, 2025March 5, 2024 by Maged kamel
brief description of post 8 content.

How to drive Crout’s LU decomposition for a 2×2 matrix? Step-by-step introduction to Crout’s LU decomposition with a solved problem.

Categories Solution of linear systems Tags Introduction to Crout's LU decomposition for a 2x2 matrix

6a- Easy approach to permutation matrix-part 2

October 21, 2025November 22, 2023 by Maged kamel
An easy approach to permutation matrix-part 2.

In the Permutation matrix-part 2, we continue the discussion about the various types of Permutation matrices.

Categories Solution of linear systems Tags Permutation matrices for a 3x3 matrix.

6- Easy introduction to permutation matrix

October 21, 2025November 22, 2023 by Maged kamel
An easy 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.

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

October 21, 2025January 20, 2021 by Maged kamel
Second solved problem-LU decomposition-3×3 matrix.

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

October 21, 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.

September 17, 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?

September 17, 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-Doolittle's method.

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

October 12, 2025November 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?

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

September 22, 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

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