## Introduction to LU Decomposition Calculator

The LU calculator is an online tool that evaluates the matrix into lower triangular and upper triangular forms. It reduces the matrix into echelon form by applying different row or column operations. It helps find the solution to a given system by making the expansion method easier.

In matrix algebra, you often have to use the echelon form method for different purposes. The LU factorization method converts the matrix into lower or upper triangular form. Here we introduce a tool that can compute and find LU factorization of a given matrix.

## The Formula used by Matrix LU Decomposition Calculator

The LU factorization refers to the factorization of a matrix into two factors, lower and upper triangular matrices with proper row or column orderings. Let A be a square matrix of order3-by-3 then,

$$ A = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \\ \end{bmatrix} $$

The LU decomposition of a matrix A can be written as:

$$ A \;=\; LU $$

Where,

$$ L = \begin{bmatrix} a & b & c \\ 0 & e & f \\ 0 & 0 & i \\ \end{bmatrix} $$

And

$$ L = \begin{bmatrix} a & 0 & 0 \\ d & e & 0 \\ g & h & i \\ \end{bmatrix} $$

L = Lower Triangular Matrix

U = Upper Triangular Matrix

The matrix decomposition calculator uses the above formula for the LU factorization of a matrix and to find the lu decomposition. It reduces the matrix into the lower triangular matrix by making all entries zero below the diagonal elements, similarly to the upper triangular matrix.

## How to use LU Factorization Method Calculator

It is easy to factorize a matrix into lower and upper triangular forms using the LU decomposition calculator, because it contains simple steps. These steps are:

- In the first step, you need to select the number of rows and columns from the respective options.
- Now enter all of the matrix entries, or you can also use the random button to select a random example.
- Click on the calculate button.

After clicking the calculate button, the given matrix will be factorized into lower and upper triangular matrices within a few moments.

## Why use LU Factorization Calculator?

In mathematics, the matrices are important to solve many problems. The matrices are mostly used to solve any system of linear equations. The LU decomposition is also applied to matrices to speed up the solution. While calculating LU factorization, sometimes you can get stuck on applying rows or column operations. Here, the LU factorization calculator can help you find the solution without losing time and energy.

## Benefits of using LU Decomposition Method Calculator

The LU decomposition is necessary for breaking the matrix into two matrices to approach the solution faster than usual. But an online tool can make the result quicker because of its amazing features. It has many useful uses, such as:

- It allows you to practice with different examples by providing a random button to find the lu decomposition.
- Matrix decomposition calculator can save your time by solving the matrix quickly.
- It is reliable because there is no chance of error in its performed steps to find lu factorization.
- LU factorization calculator is a free tool; you don’t need to subscribe to any package to use it.
- It is easy to use because of its simple steps.
- LU decomposition calculator provides a step-by-step solution so that you can understand the concept.

## FAQ’s

**What is the “Random” button?**

The random button provides you with unexpected values of a matrix so that you can practice with it. This LU calculator feature helps you understand the concept more easily.

**What is a Square Matrix?**

A matrix is a square matrix if it has the same number of rows and columns. i.e., if the number of rows and columns is equal, it is a square matrix.