Pre-calculus

PRECALCULUS - MATRICESPrecalculus - MatricesPRECALCULUS - MATRICES page 1 OF 4The invention of matrices has often been credit to a Japanese mathematician named Seki Kowa . In a scholarly tap he kindered in 1683 he discussed his study of magic squ atomic number 18s and what would come to be called determinates . Gottfried Leibniz would also independently write on matrices in the meticulous late 1600s (O Conner and Robertson 1997 ,. 1The reality is that the concept of matrices predates these fairly modern mathematicians by about 1600 eld . In an ancient Chinese inculcate text titled Nine Chapters of the Mathematical Art , indite quondam(prenominal) between 300 BC and 200 AD , the rootage Chiu Chang Suan Shu provides an framework of utilise hyaloplasm operations to solve co-occurrent equations . The opinion of a determinate appears in the work s 7th chapter , swell over a thousand years beforehand Kowa or Leibnitz were credited with the idea . Chapter eight is titled Methods of rectangular Arrays . The mode described for solving the equations utilizes a counting room that is same to the modern mode of solution that Carl Gauss described in the 1800s That method , called Gaussian ejection , is credited to him , almost 1800 years after(prenominal) its true (Smoller 2001 ,. 1-4In what we will call Gaussian Elimination (although it rattling should be called Suan Shu Elimination , a governance of linear equations is write in hyaloplasm form . Consider the dodging of equations This is define into intercellular substance form as three divers(prenominal) matrices PRECALCULUS - MATRICES foliate 2 OF 4 . But it can be work without using matrix multiplication directly by using the Gaussian Elimination procedures .

First , the matrices A and C are joined to form one augmented matrix as such A series of elementary courseing operations are wherefore used to reduce the matrix to the words echelon form This matrix is past written as three equations in conventional form The equations are then solved sequentially by substitution , starting by substituting the chousen range of z (third equation ) into the guerilla equation , solving for y , then substituting into the offset printing equation , then solving for x , yielding the 1993 , pp 543-553Before we foreshorten all of this work , it is important to determine if the dodging of equations has a solution , or has an infinite number of solutions . As an example of a placement of equation s that has no solution consider this organization of linear equations PRECALCULUS - MATRICES PAGE 3 OF 4Written in the augmented matrix form , this system isMultiply course of study 1 by -2 and kick in it to row 2Multiply row 1 by -2 and cast up it to row 3Swap row 2 and row 3Multiply row 2 by -5 and add it to row 3Multiply row 3 by -1 /10Multiply class 2 by -2 Since the reduced matrix has an equation we know to be false , 0 1 , we know that this system does non have a solution (Demana , Waits Clemens 1993 , pp 543-553PRECALCULUS - MATRICES PAGE 4 OF quarto illustrate a system...If you want to get a luxuriant essay, order it on our website: OrderCustomPaper.com

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