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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.

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

June 18, 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

June 18, 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.

January 4, 2024December 1, 2020 by Maged kamel
Derive the expression for L-U values for-3×3 matrix.

Step-by-step guide on how to derive the expression for L-U values for-3×3 matrix? Matrix A is converted to U1 and L1 matrix, then to L2 and U2 matrix.

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?

March 21, 2024November 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-Cholesky.

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

May 11, 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?

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

March 21, 2024October 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 Linear systems of Equations.
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Case 2 for block Shear-Coped Beam Problem (1) CB value-bracing at the midpoint of a beam-uniform load (1) CB value-bracing at third points of a beam-uniform load (1) Deflection of steel beams (3) Discontinuity functions table for loads (2) Effective length factor for an inelastic column. (1) Find deposit value for uniform series? (1) How to design a steel beam? (1) Inertia Ix for Parallelogram. (2) introduction to Tension members (2) list of steel beams posts-part -4a (1) LU-partial pivoting (2) Mohr's circle of inertia part 2 (2) Moment of inertia Ix for the Trapezium-second option (1) Part 1 of the Solved problem 5 for design shear strength (1) Part 2 of solved problem 5 for design shear strength (1) Permutation matrix. (2) Practice problem for the x and y coordinates of a trapezoid (1) Simple interest and compound interest (2) Solved problem-7-4-1 (1) Solved problem 5-2 for the plastic moment value for W10x60. (1) Solved problem 7-2 for frames 1-3 (1) Solved problem 8-32, finding the plastic nominal load (2) Solved problems for the net area. (2) steel beam posts part -2a (1) Two Practice problems for inertia for trapezium. (1) Two Practice problems for Ixy for trapezium (1) video-Iy and polar moment of inertia for case 2-right angle. (1) Video for Ix for a right-angle triangle (1) Video for Ixy for a rectangle section. (1) Video for Ixy for a right-angle triangle case 1. (1) Video for Ixy for a triangle (1) Video for practice problem-2 for the moment of inertia. (1) x bar for a right angle triangle (2) y bar for a right angle triangle by integration. (2)

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