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Row Reduction on Excel Row Reduction on Excel

Row Reduction on Excel - PowerPoint Presentation

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Row Reduction on Excel - PPT Presentation

Michael D Smith Lycoming College January 8 2016 Outline Why I chose Excel When I teach Excel How I teach Excel First Reason for Using Excel I allow my students to swap labeled columns in a matrix ID: 583604

columns excel generator row excel columns row generator system students teach matrix problem linear labels technology equations echelon number

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Slide1

Row Reduction on Excel

Michael D. Smith

Lycoming College

January 8, 2016Slide2

Outline

Why I chose Excel

When I teach Excel

How I teach ExcelSlide3

First Reason for Using Excel

I allow my students to swap labeled columns in a matrix.

This gives a total of four elementary operations:

Interchange any two rows

Interchange any two columns and labels to the left of the bar

Multiply any row by a nonzero number

Add any multiple of one row into another row

The built in RREF commands on Maple and Mathematica don’t have this.Slide4

Aside … Why Allow Swapping Columns

1) It is legal provided that one switches the labels as well.

2x+3y=12 is the same equation as 3y+2x=12.

2) Allowing the column swap is a tradeoff.

One gains the following:

The ability to line up all pivot columns before any non-pivot columns.

A echelon form where it easier to determine free and basic variables.

A cleaner explanation of the Simplex Algorithm.

One only loses the uniqueness of reduced row echelon form.Slide5

Second Reason for Using Excel

Excel serves as a happy medium on the technology continuum.

On one end is the no technology belief.

On the other end is the belief that row reduction is of minimal importance in matrix and linear algebra and should be relegated to a computer algebra system after the first few classes.

Excel will do all the arithmetic but will not do the whole problem.

The student still has to key in the row/column operations.

This means the student still has to know what operation(s) to do next.

Slide6

When I Teach Excel

Monday of the third week of classes.

I spend one class period in the computer lab.

Students have to row reduce by hand for the first two weeks.

Students have to complete the first two quizzes without Excel.

The first exam is given in two parts … one with and one without Excel.

On the non-excel part, students have to solve three systems … one with zero solutions, one with one solution, and one with infinite solutions.

From then on, the use of Excel is allowed and strongly encouraged.Slide7

Setting up Excel

You will need 5 columns + the number of variables in your system.

Highlight and center all of these columns. Wrap Text.

For stylistic purposes, paint all of these columns white.

Select the first four columns and put them in text mode.Slide8

Example

We will work through the following system of linear equations:

Link to Excel DocumentSlide9

Problem Generator

I have made the following problem generators on Excel:

System of Linear Equations Generator

Leontief Model Generator

Simplex Algorithm Generator

Eigenvector / Eigenvalue Generator

Markov Chain Generator

Leslie Matrix

Generator

Email me at

smithm@lycoming.edu

and I will share a copy

with you.