Math teaching opinion - Matrices

[MarkT]

How useful/important is learning the elementary row operations/augmented matrix method for finding the inverse of a 3X3 matrix?

Brown Precalc book circa 2003 shows 2X2 with determinants method and says 3X3 and higher is for computers.

I think I agree after attempting a row operations walk-through with DS and getting wrapped around my axel.

 

In the end I just went here and did the "Show details" choice:
http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi

:coolgleamA:

 

I stated that the important part is setting up the matrices and the computer will do the tedious parts for you.

What do y'all think?

Edited July 15, 2016 by MarkT

[regentrude]

At high school level, completely unnecessary IMO.

For students who will need this, they should cover that in Linear Algebra. Being able to find the inverse of a matrix without a computer can be useful for a select few, but can wait several more years for those students.

 

I would cover the basic idea of the inverse of a matrix and illustrate with 2x2; that is entirely sufficient.

 

Edited July 15, 2016 by regentrude

[Arcadia]

Are you using the Gauss-Jordan method? My opinion is that it is useful to work out the inverse of a 3x3 matrix without a calculator just for the experience. Just treat it as a warm up exercise.

 

3x3 matrix is common in finite element modelling so it was nice that I already had the drill to do it for engineering class without a calculator.

 

https://www.mathsisfun.com/algebra/matrix-inverse-row-operations-gauss-jordan.html

 

My older does the inverse by hand then use his ti-84 to check for fun.

[kiana]

I agree with regentrude 100%. I don't do this beyond 2x2 in the precalc class at university. I mention that it works for bigger ones. The few who will need it will get it in linear. For the rest it's a tedious exercise in fractions and frustration. 

 

I focus the precalc class pretty heavily on:

a) tools they will need for calculus

b) tools they will need for physics

c) concepts of mathematics as a discipline rather than a collection of arbitrary rules made up by mathematicians to torture students

 

So I do do the proofs of many things, because I want to show why it's true rather than tell them that it's true and make them practice it. I want to show that there's a reason that these things are the way they are. But to make time for this I need to cut down on some of the sections. 

[Arcadia]

I don't do this beyond 2x2 in the precalc class at university.

OT:

Why is Gauss-Jordan Elimination not taught alongside Cramer's Rule before precalc at high school where there is less time crunch.

[regentrude]

OT:

Why is Gauss-Jordan Elimination not taught alongside Cramer's Rule before precalc at high school where there is less time crunch.

 

When do you teach Cramer's rule before precalc?

AoPS covers it in the Precalculus book.

[Arcadia]

When do you teach Cramer's rule before precalc?

AoPS covers it in the Precalculus book.

AoPS intro to algebra's chapter 5's challenge problem on page 155. Also Larson's algebra 2 California edition before common core started.

 

ETA:

ApPS intermediate algebra's chapter 1's challenge problem on page 23

Edited July 18, 2016 by Arcadia