Exploring the Impact of Gaussian Elimination: A Comprehensive Analysis

[Debi78]

My linear algebra teacher is strange. This is proof, he wants us to write a 4 page essay about the strengths and weaknesses of the Gaussian Elimination method to solve systems of equations covering these four areas: accuracy, student understanding, preparation for higher-level mathematics, and use of technology.

I have some idea for each area except for the student understanding and preparation for higher-level mathematics. This is what I have and I am wanting to see how it sounds.

Accuracy
Strengths:

• determine if a system is consistent
• removes the need to rewrite the variables with each step
• easier to solve

Weaknesses:

• difficult by hand when there are more than 4 equations
• can have accuracy problems when rounding decimals

Student Understanding
Strengths:

• reinforces the idea that a system of equations work together

Weaknesses:

• very little experience working with matrices
• tendency to want to skip steps

Preparation for higher-level mathematics
Strengths:

• increases the understanding of concepts involving matrices
• prepares the students to think mathematically at a higher level

Weaknesses:

• need ideas

Use of technology
Strengths:

• helps students to check the work they did by hand
• prepares the students for using matrics in other courses such as computer science and physics

Weaknesses:

• students relying too heavily on using technology before they have a full understanding of the concepts
• can sometimes still have errors when rounding decimals

I am wondering how does this sound and if anyone has any suggestions to add or to change.

Thank you,
Debi

 

[CFDFEAGURU]

Under Accuracy - Weaknesses I would list the following facts.

1. All of the right hand side values must be known in order to use the method.
2. Only works on square matrices.
3. Fails if you end up with a singular matrix.

Under Accuracy - Strengths I would list the following facts.

1. Can find the matrix inverse easily.

Under Student Understanding - Strengths

1. This is the easiest method to comprehend
2. Very easy to program the method in C, C++, Java, etc ...
3. Sets the foundation for more advanced techniques such as Lower Upper Decomposition

Under Student Understanding - Weaknesses

1. At first it seems boring. lol

You have good points in the other sections. Linear algebra is everywhere in applications of physics.

4 pages seems a little long on just Gaussian Elimination so good luck in stretching it out.

Thanks
Matt

 

[Debi78]

Thank you Matt. I still need some ideas for the student preparation for higher level mathematics area.