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
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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.