Pre-calculus

PRECALCULUS - MATRICESPrecalculus - MatricesPRECALCULUS - MATRICES rascal 1 OF 4The invention of matrices has often been credit to a Japanese mathematician named Seki Kowa . In a scholarly civilize he leapered in 1683 he discussed his study of magic squ ares and what would come to be called determinates . Gottfried Leibniz would also independently write on matrices in the precise 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 drill text titled Nine Chapters of the Mathematical Art , scripted quondam(prenominal) between 300 BC and 200 AD , the indite Chiu Chang Suan Shu provides an framework of exploitation hyaloplasm operations to solve co-occurrent equations . The judgment of a determi nate appears in the work s 7th chapter , strong over a thousand years beforehand Kowa or Leibnitz were credited with the idea . Chapter eight is titled Methods of rectangular Arrays . The manner described for solving the equations utilizes a counting room that is uniform to the modern outline of solution that Carl Gauss described in the 1800s That method , called Gaussian ejection , is credited to him , almost 1800 years afterward its true (Smoller 2001 ,. 1-4In what we will call Gaussian Elimination (although it really should be called Suan Shu Elimination , a governance of linear equations is compose in hyaloplasm form . Consider the dodging of equations This is format into intercellular substance form as three divers(prenominal) matrices PRECALCULUS - MATRICES scalawag 2 OF 4 . But it can be work out 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 line echelon form This matrix is then(prenominal) written as three equations in conventional form The equations are then solved sequentially by substitution , starting by substituting the chousen regard as 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 remains of equations that has no solution consider this system of linear equations PRECALCULUS - MATRICES PAGE 3 OF 4Written in the augmented matrix form , this system isMultiply rowing 1 by -2 and kick in it to row 2Multiply row 1 by -2 and summate 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 not have a solution (Demana , Waits Clemens 1993 , pp 543-553PRECALCULUS - MATRICES PAGE 4 OF quarto illustrate a system...If you want to get a overflowing essay, order it on our website: OrderCustomPaper.com

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