Math 120 - Finite Mathematics
	Calculator Instructions  Technology Matrices      TI-83 or TI-82

This sheet is designed to give you instruction on how to use your calculator to solve technology matrix equations.

Scenario: The technology matrix A is given for two sectors of the economy, water and electricity. The external demand matrix D is also given.

W E

A = and D =

From class discussions, you know you can find the production matrix, X = , by solving X = (I - A)^-1D, where I = , the 2 X 2 identity matrix.

First, consider the system in matrix form.

= This is the form X = (I - A)^-1D.

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 four entries from matrix A into the matrix.

II. Enter matrix B = into the calculator. You are using B instead of I.

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 four entries from matrix B into the matrix.

III. Enter matrix D = into the calculator.

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

highlight 4, then press . This action selects matrix D to edit.

B. Enter the four entries from matrix B into the matrix.

2. Finding the production matrix X on the calculator.

To solve this system using matrix inversion you need X = (B - A)^-1D. You will use the calculator to evaluate the right hand side. Remember we are using B in place of I.

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

II. You need to evaluate (B - A)^-1D.

(

A. To do this, first insert the right parenthesis by pressing . Next, press 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.

-

B. Next, press to insert the subtraction symbol. Press to get to the matrix name menu and . This action will place

)

the matrix name [ A ] on the right side of the expression. Next close the parenthesis by pressing

2. Finding the production matrix X on the calculator cont.

C. Take the inverse of B – A by pressing .

D. You need to add matrix D to the right side by pressing to get to the matrix name menu. Press to highlight 4, then press . This action will place the matrix name [ D ] on the home screen to the right. Finally, press to evaluate the expression

Conclusion: X = = (B - A)^-1D = . So

x₁ = 27000 units of water and x₂ = 22000 units of electricity

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