## Saturday, February 1, 2014

### Pre-calculus

PRECALCULUS - MATRICESPrecalculus - MatricesPRECALCULUS - MATRICES knave 1 OF 4The invention of matrices has often been credit to a Japanese mathematician named Seki Kowa . In a scholarly pretend he gradeered in 1683 he discussed his study of magic squ bes and what would come to be called determinates . Gottfried Leibniz would also independently write on matrices in the critical 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 instill text titled Nine Chapters of the Mathematical Art , create verbally quondam(prenominal) between 300 BC and 200 AD , the informant Chiu Chang Suan Shu provides an framework of utilise hyaloplasm operations to solve co-occurrent equations . The cerebration of a determinate appears in the work s 7th chapter , healthful over a thousand years beforehand Kowa or Leibnitz were credited with the idea . Chapter eight is titled Methods of rectangular Arrays . The method acting acting described for solving the equations utilizes a counting room that is undistinguishable to the modern method 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 very should be called Suan Shu Elimination , a governance of linear equations is create verbally in hyaloplasm form . Consider the dodging of equations This is target into intercellular substance form as three divers(prenominal) matrices PRECALCULUS - MATRICES rascal 2 OF 4 . But it can be resolved without using matrix multiplication directly by using the Gaussian Elimination procedures . First , the matrices A and C argon joined to form one augmented matrix a! s such A series of elementary courseing operations are wherefore used to reduce the matrix to the form echelon form This matrix is thus written as three equations in conventional form The equations are then solved consecutive by substitution , starting by substituting the chousen abide by 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 arrangement of equations that has no solution consider this strategy of linear equations PRECALCULUS - MATRICES PAGE 3 OF 4Written in the augmented matrix form , this system isMultiply track 1 by -2 and kick in it to row 2Multiply row 1 by -2 and summarise 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 climb essay, order it on our website: OrderCustomPaper.com

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