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Math teaching opinion - Matrices

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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:



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 by MarkT
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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 by regentrude
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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.




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

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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. 

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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.



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

Edited by Arcadia
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