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This procedure has been around for a very long time.
A Chinese scholar wrote a book on how to do this more
than 2000 years ago.
Several other people independently rediscovered the
method in later centuries.
Gauss popularised the method in the early 1800s and his
name is attached to it as a result.
‘Gaussian elimination’ is taught in schools and universities
all round the world today.
Computers are programmed to use the method on really
large linear systems.
Using this same procedure, they can solve systems
involving hundreds or even thousands of unknowns, in
less time than it takes you to read this sentence.
But there are better ways, and still better ways are being
discovered all the time.
Linear algebra is a big field of study today, and it’s as
much about programming machines as it is about solving
A typical space journey requires repeatedly solving
equations using 7 variables: position in each of 3
directions, speed in each of 3 directions and a clock time.
The variables are put into a 7x7 matrix and identified
using procedures similar to what you’ve just
seen, advancing the clock time by maybe one second at a
time across a journey that may take many months, so that
hundreds of thousands of repetitive matrix calculations
might be required to find out where the spacecraft ends
You can even calculate the motions of the planets using
this sort of mathematics. Gauss used matrices to plot the
motion of the asteroid Pallas, which is how he came to be
interested in the subject in the first place.
You could say, therefore, that you discovered matrices
because I discovered matrices, because my teachers
discovered matrices, because somewhere back in that
chain of teachers, Gauss demonstrated how useful the
method could be, because he was interested in a tumbling
rock in the sky some 50 million miles away.
The next question would be, who will you teach this
subject to? And what will your student’s students
discover, someday, using Gauss’s matrix method?
-David C, 2013