Education Technology

Matrices and Vectors

Published on 06/09/2008

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.

    Follow the Activity procedures:

  • 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