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.