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First found in China, India, and Japan,
the magic squares have served as art
or entertainment and even as
possessing marvelous powers; they are thought as the origin to the discovery of matrices (McKay, n.d.). Image is a Magic Square Puzzle Inscribed on Temple Pillar (Holloway, 2018). -
Historically, the
first use of matrix methods to solve
systems of equations is found in the
Chinese text, The Nine Chapters on
the Mathematical Art, written during
the Han Dynasty from 202 B.C. to 200
A.D -
"Albrecht Durer’s 1514 engraving titled Melencolia I contains a 4 × 4 magic square, the first to be seen in European art" (McKay, n.d).
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Gabriel Cramer, a Swiss mathematician, worked out a method
for solving in n algebraic equations in n unknowns (McKay, n.d.). -
Franklin created a 16 x 16 square, although he created other squares, this one is viewed as spectacular since the columns and rows add to 2,056. When half rows and half columns are added together, the sum is 1,028 (Hurley, n.d).
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May be only as a hobby, Euler developed the basics of 'Sudoku' which he termed 'Graeco-Roman Squares' or Latin Squares ➚ - he used letters as the grid square symbols rather than numbers. He mused on what would happen if you removed the rule for magic squares that the sum of the diagonals must add up to the same number as the rows and columns and turn it into a puzzle of permutations (Sudoku Dragons, n.d.).
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Carl Gauss created an algorithm for finding the general solution of a system of linear equations by reducing the augmented matrix to a triangular form (McKay, n.d.). (Image from Singh, A. (2019, December 24). Carl Friedrich Gauss - The Prince Of Mathematics, A Great Genius. Retrieved May 31, 2020, from https://mobygeek.com/features/carl-friedrich-gauss-prince-of-mathematics-10805)
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The term matrix was coined in 1850 by
James Joseph Sylvester, an English
mathematician. -
Wilhelm Jordan,a German mathematician, made some
modifications of the Gauss algorithm, which is known as the Gauss-Jordan elimination method (McKay, n.d). Photo of Wilhelm Jordan (Alamy, 2008). -
The method is utilized to solve system of equations in Linear Algebra. It also can be applied to solve and investigate situations in Environmental Science (Prince & Angulo, 2015). Also, it can used in channel decoding algorithm, Robust Fingerprint Image, use for for solving linear equations on mesh-connected processors, and in scheduling algorithms (Saeed et al., 2015).
