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Solving Systems using Matrices - Problem 1

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

To solve a system of equations using matrices, start by making sure the variables are in the same order (i.e., the x and y variables are aligned) and are equal to the constant. Write two matrices, A and B, that will be inputted into your calculator. Matrix A will be the coefficients of the two equations and matrix B will be the constants. Input the matrices into your calculator to perform the product inverse of A multiplied by B, which will give you the solutions. On your graphing calculator, click on matrix and edit matrices A and B. Input your dimensions for matrix A (2 by 2) and input the coefficients -- x and on first row, y on the second row. Input matrix B by first indicating the dimensions (2 by 1) and input the constants. Next, go the homescreen and type in the inverse of matrix A times matrix B. In the solution, the first value will be x and the second value will be y, since that was how it was entered into the calculator.

I want to solve this system of equations using matrices. You could also solve this using graphing, substitution or elimination, but these instructions tell us to use matrices.

So the first thing I'm going to do is make sure that my variables are in the same order and they are x then y. Next thing I'm going to make sure is that it's equal to my constant. Okay so these are both in the same form.

In a second I'm going to be inputting two matrices into my graphing calculator. Matrix A is called the coefficient matrix and it's going to look like this -2, 15 those are the coefficients for my first equation and then 7, -5. That's going to go into my calculator as matrix A.

Matrix B is going to be my constant matrix, it's what these equations are equal to, -32 and 17. Then I'm going to use my calculator to perform the product inverse of A multiplied by B and that's going to give me my solutions.

All right take out your graphing calculators let's do it. When you turn on your graphing calculator you usually see the home screen like this. I'm going to get into the matrix location and I'm going to want to edit my matrices A and B so I'm going to air over to edit select matrix A and it's asking me for the dimensions. My dimensions for matrix A are going to be 2 by 2.

Let's go ahead and get in there my coefficients. My coefficients are -2 and 7, those represent my different coefficients for x. Then in my second column I have my two different coefficients for y.15 and -5.

Okay so all I've done so far is input my coefficient matrix A, now that's going to say it for me. I'm going to go back input matrix B. Wait let me just double check I got matrix A correct because that looks kind of funny. Let me go back and just edit matrix A again the way you can see it is by going like that, good. I'm just double checking and making sure that these are the coefficients I wanted.

Okay let me go back and do matrix B. Going back to my matrix menu I'm going to arrow over to edit and I'm going to select matrix B its asking me to tell the dimensions. The dimensions for matrix B are 2 by 1 and then I'm going to go in and enter my constants. My constants were -32 from my first equation and the 17 from my second equation.

Okay I've done the hard stuff already I have my matrices ready to go the next thing I need to do is to go back to my home screen and I'm going to compute the product inverse of A times B. So I'm going to tell it to use matrix A. This little button here represents inverse that's one way to find the inverse, your teacher will show you other ways.

Then I'm going to multiply that by matrix B. Just go to matrix matrices select matrix B. There we go here we come back to hit enter and its going to do inverse of A times B. There it is, those are my answers you guys.

This tells me my x value is 1 my y value is -2. x comes first y comes second because that's how I in-putted them to my coefficient matrix. You guys can check this using substitution or elimination but I'm pretty confident that the calculator did it correctly. That's why I like using the calculator in matrices to solve systems of equations.

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