Mandi McGaha
Matrices and Determinants
•
300 BCThe Babylonians studied problems that lead to simultaneous linear
equatios
•
Between 200 BC and 100 BCChinese come much closer to matrices with the text
Nine Chapters on the Mathematical Art
, written during the Han Dynasty.
This
text gives the first known example of matrix methods
•
1545 Cardan gives a rule for solving a system of two linear equations and calls is
regula de modo
.
This rule is essentially Cramer’s rule for solving a 2x2 system
without the final step.
•
1660 de Witt published
Elements of Curves
, part of the commentaries on the
Latin version of Descartes’
Geometrie
.
This article showed how a transformation
of the axes reduces a given equation for a conic to canonical form.
•
1683 Seki, from Japan, wrote
Method of Solving the Dissimulated Problems
which contained matrix methods written as tables, as the Chinese had suggested,
and introduced the idea of the determinant
•
1683 Leibniz wrote to de l’Hopital explaining that the systemof equations
10+11x+12y=0
20+21x+22y=0
30+31x+32y=0
had a solution because when written in matrix form:
10.21.32+11.22.30+12.20.31=10.22.31+11.20.32+12.21.30—the first number
corresponding to the row it belonged to, the second to the column.
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 Spring '08
 Greenwald
 Linear Algebra, Determinant, Matrices, Vector Space, Mandi McGaha Matrices

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