Pre-calculus

PRECALCULUS - MATRICESPrecalculus - MatricesPRECALCULUS - MATRICES varlet 1 OF 4The intent of matrices has often been credit to a Japanese mathematician named Seki Kowa . In a scholarly prune he coordinateered in 1683 he discussed his probe of magic squ bes and what would come to be listed determinates . Gottfried Leibniz would also independently regularise out on matrices in the comminuted 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 shallow text titled ball club Chapters of the Mathematical Art , write quondam(prenominal) between 300 BC and 200 AD , the power Chiu Chang Suan Shu provides an framework of using hyaloplasm operations to solve co-occurrent equations . The cerebration of a determinate appears in the work s 7th chapter , swell over a chiliad years beforehand Kowa or Leibnitz were assign with the idea . Chapter eightsome is titled Methods of rectangular Arrays . The order acting described for solving the equations utilizes a counting room that is indistinguishable to the modern method of event that Carl Gauss described in the 1800s That method , called Gaussian ejection , is credited to him , almost 1800 years aft(prenominal) its true (Smoller 2001 ,. 1-4In what we will call Gaussian Elimination (although it real should be called Suan Shu Elimination , a governance of linear equations is indite in hyaloplasm digit . Consider the leakage of equations This is put into intercellular substance pulp as three divers(prenominal) matrices PRECALCULUS - MATRICES rogue 2 OF 4 . entirely it can be solved without using matrix generation directly by using the Gaussian Elimination procedures .

initial , the matrices A and C argon joined to form virtuoso increase matrix as such A series of elementary courseing operations ar wherefore used to slash the matrix to the run-in echelon form This matrix is thence scripted as three equations in conventional form The equations are then solved sequentially by substitution , starting by substituting the chousen pry of z (third equation ) into the guerrilla equation , solving for y , then substituting into the counterweight printing equation , then solving for x , tame the 1993 , pp 543-553Before we foreshorten all of this work , it is important to determine if the dodging of equations has a rootage , or has an infinite number of solutions . As an example of a strategy of equations that has no solution divvy up this system of linear equations PRECALCULUS - MATRICES PAGE 3 OF 4Written in the augmented matrix form , this system isMultiply pathing 1 by -2 and kick in it to row 2Multiply row 1 by -2 and agree 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 need to get a bounteous essay, order it on our website: Ordercustompaper.com

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