# 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.

## 7-A Solved problem 9-5 LU decomposition.

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

## 6- 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.

## 5A- 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?

## 5- First solved problem-LU decomposition for the 3×3 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?

## 4-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.

## 3-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.

## 2- 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?

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

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