Education Technology

# Activities

• ##### Subject Area

• Math: Algebra I: Matrices

College

60 Minutes

• TI-86
• ##### Other Materials
This is Activity 7 from the EXPLORATIONS Book: Using the TI-86 in Collegiate Mathematics: A Tutorial

## Matrices and Vectors

#### Activity Overview

In this activity, students learn to create and edit a matrix using the matrix editor. They use various features in the calculator to perform elementary row operations and convert a matrix to its reduced row echelon form. Finally they verify important results and solve a variety of problems in matrix theory and linear algebra.

#### Before the Activity

• Set up the calculator as explained in the activity
• See the attached PDF file for detailed instructions for this activity
• Print pages 91 - 101 from the attached activity PDF file for the class
• #### During the Activity

Distribute the pages to the class.

• Create a matrix using the matrix editor, or from the home screen
• Use the calculator to perform matrix-vector multiplication, and recognize the fact that the result will be a vector
• Understand submatrices, and study matrix arithmetic
• Use the matrix editor to edit a matrix

• Create a matrix with complex number entries, and form its conjugate
• Add the matrix and its conjugate, and store the result
• Edit the result in the matrix editor and convert it into a real matrix

• Create a matrix and reduce it to its echelon form using elementary row operations
• Redimension the matrix by adding columns of zeros, if it has more rows than columns
• Convert the entries in the row-reduced echelon form to fractions

• Create a square matrix, and use the features of the calculator to determine its Eigen values and Eigen vectors
• Use the Power Method to find the dominant eigen value and a corresponding eigen vector for the square matrix

• Use the Gram-Schmidt process for finding an orthogonal basis
• #### After the Activity

Students complete the exercises on the Activity sheet.

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary