Page 10 - Matrix Analysis & Applied Linear Algebra

2 Chapter 1 Linear Equations

a square array on a “counting board” and then manipulated the lines of the
array according to prescribed rules of thumb. Their counting board techniques
and rules of thumb found their way to Japan and eventually appeared in Europe
with the colored rods having been replaced by numerals and the counting board
replaced by pen and paper. In Europe, the technique became known as Gaussian
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elimination in honor of the German mathematician Carl Gauss, whose extensive
use of it popularized the method.
Because this elimination technique is fundamental, we begin the study of
our subject by learning how to apply this method in order to compute solutions
for linear equations. After the computational aspects have been mastered, we
will turn to the more theoretical facets surrounding linear systems.

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Carl Friedrich Gauss (1777–1855) is considered by many to have been the greatest mathemati-
cian who has ever lived,and his astounding career requires several volumes to document. He
was referred to by his peers as the “prince of mathematicians.” Upon Gauss’s death one of
them wrote that “His mind penetrated into the deepest secrets of numbers,space,and nature;
He measured the course of the stars,the form and forces of the Earth; He carried within himself
the evolution of mathematical sciences of a coming century.” History has proven this remark
to be true.