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 race he yearered in 1683 he discussed his study of magic squargons and what would come to be called determinates . Gottfried Leibniz would also independently write on matrices in the dead 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 teach text titled Nine Chapters of the Mathematical Art , compose quondam(prenominal) between 300 BC and 200 AD , the compose Chiu Chang Suan Shu provides an framework of employ hyaloplasm operations to solve co-occurrent equations . The composition of a determinate appear s 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 body described for solving the equations utilizes a counting room that is superposable to the modern order of solution that Carl Gauss described in the 1800s That method , called Gaussian ejection , is credited to him , almost 1800 years later its true (Smoller 2001 ,. 1-4In what we will call Gaussian Elimination (although it genuinely should be called Suan Shu Elimination , a governance of linear equations is compose in hyaloplasm form . Consider the dodging of equations This is vex into intercellular substance form as three divers(prenominal) matrices PRECALCULUS - MATRICES rogue 2 OF 4 . But it can be puzzle out without using matrix multiplication directly by using the Gaussian Elimination procedures .

First , the matrices A and C atomic number 18 joined to form one augmented matrix as such A series of elementary courseing operations are wherefore used to reduce the matrix to the actors line echelon form This matrix is indeed written as three equations in conventional form The equations are then solved consecutive by substitution , starting by substituting the chousen observe 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 brass of equations that has no solution consider this system of linear equati ons PRECALCULUS - MATRICES PAGE 3 OF 4Written in the augmented matrix form , this system isMultiply wrangle 1 by -2 and kick in it to row 2Multiply row 1 by -2 and score 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 enough essay, order it on our website: OrderEssay.net

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