## How Can I Use WolframAlpha To Get Reduced Row Echelon Form?

A matrix is entered between curly brackets in WolframAlpha (http://www.wolframalpha.com). Additionally, each row of the matrix is entered in curly brackets too.

You can also put a matrix in reduced row echelon form. We could put the augmented matrix

$latex \displaystyle \left[ \begin{array}{*{35}{l}} 1 & 2 & -1 \\ 4 & 3 & 1 \\ \end{array} \right]$

Use the text “row reduce” and then enter the matrix. The solution is x = 1 and y = -1.

Let’s try this with another system of linear equations

Convert this system into a 3 x 4 augmented matrix:

WolframAlpha understands several commands for putting an augmented matrix into reduced row echelon form. You can use the command rref { }or the command row reduce { }. The matrix goes inside the curly brackets. However, the matrix must be put in carefully. Each row needs to be typed in inside of curly brackets with the entries separated by a commas. In this case, you would type

on the command line in WolframAlpha.

After you press Enter, the reduced row echelon form is computed,

This indicates that the solution to the system is

x = 65,000, y = 45,000, z = 40,000.

## How Do You Solve a Linear System with WolframAlpha?

Many of you may already be familiar with using a graphing calculator to put a matrix in reduced row echelon form. Did you know that you can do the same thing with WolframAlpha?

To see how this is done, let’s start from the system of linear equations

Convert this system into a 3 x 4 augmented matrix:

WolframAlpha understands several commands for putting an augmented matrix into reduced row echelon form. You can use the command rref { }or the command row reduce { }. The matrix goes inside the curly brackets. However, the matrix must be put in carefully. Each row needs to be typed in inside of curly brackets with the entries separated by a commas. In this case, you would type

on the command line in WolframAlpha.

After you press Enter, the reduced row echelon form is computed,

This indicates that the solution to the system is

x = 65,000, y = 45,000, z = 40,000.

## How Can You Model Data With A System of Equations (Continued)?

In an earlier FAQ, I mentioned that there was a second strategy for solving the Sony Math Problem. Recall the basic problem:

In December of 2014, Sony released the movie The Interview online after threats to theaters cancelled the debut in theaters. As originally reported in Wall Street Journal, the sales figures reported in January contained an interesting math problem appropriate for algebra students.

The following January, Sony reported sales of 31 million dollars from the sales and rentals of The Interview. They sold the movies online for 15 dollars and rented through various sites for 6 dollars. If there were 4.3 million transactions, how many of the transaction were sales of the movie and how many of the transactions were rentals?