Solution of linear systems

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

December 14, 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.

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

December 21, 2025October 29, 2024 by Maged kamel

LU decomposition for the Crout's method for 3x3 matrix-option 2

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?

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.

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

January 13, 2026March 5, 2024 by Maged kamel

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.

7-A Solved problem 9-5 LU decomposition.

December 17, 2025February 25, 2024 by Maged kamel

Solved problem 9-5 LU decomposition from reference book Numerical methods for engineers. We will verify our solution with the author’s solution.

6a- Easy approach to permutation matrix-Part 2

January 26, 2026February 10, 2024 by Maged kamel

Brief illustration of Post 6a numeric linear

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

6- Easy introduction to permutation matrix

January 25, 2026February 7, 2024 by Maged kamel

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?

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

December 17, 2025February 3, 2024 by Maged kamel

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