Math 120 - Finite Mathematics

 

 

 

 

Calculator Instructions
    Matrix Inversion
     TI-83 or TI-82

 

 

 

 

 

 

 

 

This sheet is designed to give you instruction on how to use your calculator to solve a system of equations using matrix inversion.

 

Scenario: Your math teacher asks you to solve the following system of equations.

 

2x + 3y = 7

3x – 10y = 25

 

From class discussions, you know you can solve this system using matrix inversion. You will use the calculator to do the work.

 

First, consider the system in matrix form.

 

´ =       This is the form AX = B.

 

 

1. Enter the matrices into the graphing calculator.

 

I. Enter matrix A =  into the calculator.

 

A. Press     to get to the edit matrix menu. Next press . This action selects matrix A to edit.

 

 

    

 

 

B. Enter the dimensions of the matrix (2 X 2) at the top if the dimensions are incorrect. The calculator automatically resizes the matrix.

 

 

1. Enter the matrices into the graphing calculator cont.

 

C. Enter the four entries from matrix A into the matrix.

 

 

 

 

 

II. Enter matrix B =  into the calculator.

 

A. Press     to get to the edit matrix menu. Press  to

 

highlight 2, then press . This action selects matrix B to edit.

 

 

    

 

 

B. Enter the dimensions of the matrix (2 X 1) at the top if the dimensions are incorrect. The calculator automatically resizes the matrix.

 

 

 

 

1. Enter the matrices into the graphing calculator cont.

 

C. Enter the two entries from matrix B into the matrix.

 

 

 

 

 

2. Solving the system using matrix inversion on the calculator.

 

To solve this system using matrix inversion you need X = A-1B. You will use the calculator to evaluate the right hand side.

 

I. Get back to the home screen. Press    to get to the home screen.

 

 

II. You need to evaluate A-1B.

 

A. To do this, press     to get to the matrix name menu. Matrix A is already selected as the default. Next, press .  This action will place

 the matrix name [ A ] on the home screen.

 

  

 

 

 

2. Solving the system using matrix inversion on the calculator cont.

 

B. To take the inverse of A, press  . This places [ A ]-1 on the home

X
 
screen. Next, press                       to add the multiplication operator.

 

 

 

C. Finally, add matrix B to the right side by pressing     to get to the matrix name menu. Press  to highlight 2, then press . This action will place the matrix name [ B ] on the home screen to the right.

 

  

 

 

D. To evaluate the expression, press .

 

 

Conclusion: X =  = A-1B =   so x = 5 and y = -1

 

 

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