If you ever had to learn about row reducing, you know how helpful this mathematical technique can be for resolving a system of equations. Here’s everything you need to know about reducing a row echelon form on a TI83 or TI84 calculator.

What’s an augmented matrix?

An augmented matrix for a system of equations is commonly composed of 3 equations 3×3 with each row representing the constants from one equation. On the other hand, the columns in your augmented matrix will represent the coefficients for a single variable.

Matrix Vs Augmented Matrix

The main difference between the two is that in the augmented matrix you have an extra column on the right-hand side consisting of the different values of the coefficients. A non-augmented matrix will simply consist of a linear equation system made up of coefficients, without that extra column.

Solving an equation system on your TI Calculator

Practice makes perfect, as they say, so let’s see a real example of how to reduce a Row Echelon Form on your TI calculator:

The System

Here’s what our equation system is going to look like:

• 4x – 2y – 5z = 11
• x + y + z = 2
• -2x + 3y – 2z = -14

Converting the system to an augmented matrix

Now, we need to convert this equation system to an augmented matrix. Simply use the rref command on your TI graphic calculator, it should give you something like this:

Entering the Matrix

After you successfully converted the system into an augmented matrix, you can access the latter by following the steps below:

• Press the y— button on your calculator to access the Matrix Menu
• Select ~ to EDIT
• Press À or move the cursor to 1: [A] and confirm
• Now it’s important to enter the proper dimensions, which should be 3×4
• Enter the values and press the I button after each entry.
• Press QUIT to go back to the home screen.

Be aware that you will need to use the right arrow in order to scroll through the entirety of the matrix, since it will take 2 screens in total on your calculator TI.

Viewing the Matrix on the Home Screen

Thereafter, you are ready to access the augmented matrix that we completed in step 3 from the home screen, as shown below:

• Press the y— button on your calculator to go to the NAMES menu from the Matrix Menu.
• Move the cursor to 1: [A] and press the I button. This will put [A] on the Home screen.
• From there, you can finally view the matrix on the home screen.

Finding the reduced row echelon form of the Matrix on your TI calculator

We are finally ready to find the reduced row echelon form! Follow the instructions below:

• As always, press the y— button on your calculator to access the Matrix Menu
• Select ~ to go to MATH
• Use † to select B: rref(, then, Press I to put the rref( on the home screen.
• Now, enter the name of the matrix you created earlier in the parentheses and press the y— button to access the Matrix Menu once more.
• Press À or highlight 1: [A] and press I. This will allow you to copy-paste the name of the matrix [A] into the rref ( command from the home screen.
• As a final step, press the I button to calculate the reduced row echelon form of your augmented matrix.

Please take note that if you don’t enter the name properly in step 5, you will most likely get an ERR: DATA TYPE message. On that note, we hope this little guide was helpful and that you will be able to reduce the row echelon form of a matrix like a pro!