Looking for Matricies with their R-Echelon Forms

In summary, the conversation is about a person testing a matrix solving program and wanting to try it on larger matrices without having to manually reduce them. Another person suggests using Octave, a program that can reduce matrices of any size and provides an example of using it.
  • #1
Vorde
788
0
Hi all,

I'm testing out a matrix solving program and while it checks out for 2x2/3x3/4x4 I would like to try it out on some larger matrices, but I don't really want to go through the hassle of row reducing a couple of 10x10 matrices to double check my program.

Does anyone happen to know of a website with matrices and their reduced echelon forms? Hopefully some with sizes > 5x5 (the maximum size is only restricted by memory, but past 25x25 I get visual errors).

Thanks!
 
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  • #2
Octave (http://octave.sourceforge.net/) will do this for you.

Example:
Code: 
12 > A = randn(5,7)
A =

  -1.168059   1.379002   1.050133   1.174869   0.241811  -1.207374  -0.879474
  -1.069804  -0.276065  -0.122203   0.106788  -0.868123  -0.376758   0.843255
  -0.254340   1.737628   0.500414  -0.232824  -0.963609  -1.475793   0.405880
  -1.008958  -0.018789   0.523780   0.369066  -0.010553  -1.382835   0.084481
   0.858681  -2.586128   0.415349   0.538282   0.834653  -0.063377  -0.128834

13 > rref(A)
ans =

   1.00000   0.00000   0.00000   0.00000   0.00000   0.66988  -0.17216
   0.00000   1.00000   0.00000   0.00000   0.00000   0.20572  -0.33145
   0.00000   0.00000   1.00000   0.00000   0.00000  -2.44269   0.18477
   0.00000   0.00000   0.00000   1.00000   0.00000   1.56390  -0.54221
   0.00000   0.00000   0.00000   0.00000   1.00000   0.07930  -0.74650
 

FAQ: Looking for Matricies with their R-Echelon Forms

What is a matrix?

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is used to represent linear equations and transformations in mathematics and is an essential tool in various fields of science and engineering.

What is the R-Echelon form of a matrix?

The R-Echelon form of a matrix is a reduced row-echelon form, where the matrix is transformed into a special form by using elementary row operations. In this form, all the pivot elements (the first non-zero element in each row) are equal to 1, and each pivot element is the only non-zero element in its respective column.

Why is it important to look for matrices with their R-Echelon forms?

Looking for matrices with their R-Echelon forms can simplify and solve complex systems of linear equations, allowing for more efficient and accurate calculations. It also helps in determining the rank and invertibility of a matrix, which are important properties in many applications.

What are the elementary row operations used to transform a matrix into its R-Echelon form?

The three elementary row operations are: 1) Swapping two rows, 2) Multiplying a row by a non-zero constant, and 3) Adding a multiple of one row to another row. These operations can change the values of the entries in a matrix, but they do not change the solutions to the linear equations represented by the matrix.

Can any matrix be transformed into its R-Echelon form?

Yes, any matrix can be transformed into its R-Echelon form. However, not all matrices have a unique R-Echelon form. Matrices that have more than one pivot element in a row or a column may have multiple R-Echelon forms, but all forms are equivalent in terms of solving linear equations and determining the rank and invertibility of the matrix.

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