Gaussian Elimation with Partial Pivoting Algorithm by hand

In summary, the conversation discusses the Gaussian Elimination with Partial Pivoting algorithm applied to a given matrix, which will result in the construction of matrices P, L, and U. The defining properties of these matrices are discussed, as well as the relationship they have with matrix A. The conversation also mentions various methods and resources for solving the problem by hand, including using rref command on a Ti89 calculator and MATLAB functions.
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medinaj2160
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Homework Statement



The Gaussian Elimination with Partial Pivoting algorithm when applied to the following matrix

A[-3 0 4; 5 2 -6; 0 0 1]

Will construct matrices P, L, and U

1- What are the defining properties of the matrices P, L and U?

2- What relation do P, L, U and A always satisfy?

3- Given that

L=[1 0 0, -3/5 1 0; 0 0 1]

What are P and U?

Homework Equations



PA=LU

The Attempt at a Solution



How do I do this by hand?
There is rref command on the Ti89, the is lu(A), A\b, inv(A)*b on matlab...

Anyways I know how to get the answer by doing this http://www.youtube.com/watch?v=euIXYdyjlqo" but I don't know how to construct the matrices that he wants, this is not homework is a review for a test on Monday.

I know
P= is the permutation matrix= it switches rows
L= lower triangular matrix
U= upper triangular matrix.

So I need, to this by hand. Can someone send link or help me on how to do this step by step?

Thanks
 
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Related to Gaussian Elimation with Partial Pivoting Algorithm by hand

1. What is Gaussian Elimination with Partial Pivoting algorithm?

Gaussian Elimination with Partial Pivoting algorithm is a method used to solve systems of linear equations. It involves manipulating a matrix representation of the equations in order to reduce it to a simpler form that can be easily solved.

2. Why is partial pivoting necessary in Gaussian Elimination?

Partial pivoting is necessary in Gaussian Elimination because it ensures a more accurate solution by reducing the amount of error introduced during the elimination process. It also helps to avoid division by zero errors.

3. How does Gaussian Elimination with Partial Pivoting work?

Gaussian Elimination with Partial Pivoting works by systematically eliminating variables in a system of equations until a solution is found. It involves swapping rows and columns of the matrix to ensure that the largest coefficient is used in each elimination step, resulting in a more stable and accurate solution.

4. Is it possible to perform Gaussian Elimination with Partial Pivoting by hand?

Yes, it is possible to perform Gaussian Elimination with Partial Pivoting by hand. However, it can be a time-consuming and tedious process, especially for larger systems of equations. It is more commonly done using computer algorithms.

5. What are the benefits of using Gaussian Elimination with Partial Pivoting?

Gaussian Elimination with Partial Pivoting is a powerful method for solving systems of linear equations. It is more accurate and efficient than other methods, such as substitution or Cramer's rule. It also allows for the solution of larger and more complex systems of equations.

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