# LU Factorization on Ti-89: 3x3 & 4x4 Matrix Solutions

• Math100
In summary, LU factorization is a method used to decompose a matrix into a lower triangular matrix (L) and an upper triangular matrix (U). It can be performed on a Ti-89 calculator and is commonly used to solve systems of linear equations. To use LU factorization on a Ti-89 calculator, the matrix must first be entered into the calculator using the matrix editor. It can be used for matrices of any size, but is recommended for smaller matrices. Unlike other matrix decomposition methods, LU factorization does not involve row operations and can provide more accurate solutions. Using LU factorization on a Ti-89 calculator can save time and effort, handle large numbers and decimals, and allow for other calculations using the L and U matrices
Math100
What's the correct command for finding an LU factorization of a 3x3 and 4x4 matrix on Ti-89 graphing calculator? I'm trying to find the correct answers and verify/check my answers for Linear Algebra problems.

TI makes available a PDF of the guidebook for the TI-89 Titanium. It describes how to use the LU command.

## What is LU factorization and why is it useful?

LU factorization is a matrix decomposition method that breaks down a square matrix into two lower and upper triangular matrices. It is useful for solving systems of linear equations, calculating determinants, and inverting matrices.

## How do I perform LU factorization on a 3x3 matrix using a Ti-89 calculator?

To perform LU factorization on a 3x3 matrix using a Ti-89 calculator, follow these steps:
1. Enter the matrix into the calculator by pressing [2nd] then [MATRX] and selecting [EDIT].
2. Press [2nd] then [MATH] and select [Matrix] from the menu.
3. Select [MATH] again and navigate to [A:LU(A)].
4. Press [ENTER] to see the result, which will be displayed as [L, U] in the Home screen.

## Can LU factorization be used on non-square matrices?

No, LU factorization can only be performed on square matrices. If you have a non-square matrix, you can use other methods such as QR factorization or Singular Value Decomposition (SVD) to decompose it.

## What is the difference between LU factorization and Gaussian elimination?

Both LU factorization and Gaussian elimination are used to solve systems of linear equations. However, Gaussian elimination involves using elementary row operations to reduce a matrix to row-echelon form, while LU factorization decomposes a matrix into two triangular matrices. LU factorization is generally more efficient and accurate than Gaussian elimination.

## Can I use LU factorization on a 4x4 matrix with complex numbers?

Yes, you can use LU factorization on a 4x4 matrix with complex numbers. However, make sure your calculator is set to complex mode by pressing [MODE] and selecting [a+bi] before performing the factorization.

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