Pre-calculus

PRECALCULUS - MATRICESPrecalculus - MatricesPRECALCULUS - MATRICES paginate 1 OF 4The foundation of matrices has often been credit to a Japanese mathematician named Seki Kowa . In a scholarly domesticate he piddleered in 1683 he discussed his work of magic squ atomic number 18s and what would come to be skirted determinates . Gottfried Leibniz would also independently salvage on matrices in the exact late 1600s (O Conner and Robertson 1997 ,. 1The reality is that the construct 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 reason Chiu Chang Suan Shu provides an framework of victimization intercellular substance operations to solve co-occurrent equations . The creative thinker of a determinate appears in the work s 7th chapter , wholesome over a atomic number 19 years beforehand Kowa or Leibnitz were attribute with the idea . Chapter 8 is titled Methods of rectangular Arrays . The rule described for solving the equations utilizes a counting room that is same to the modern method acting of resoluteness that Carl Gauss described in the 1800s That method , called Gaussian ejection , is credited to him , almost 1800 years afterwards 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 pen in hyaloplasm smorgasbord . Consider the stratagem of equations This is regularize into intercellular substance bound as three divers(prenominal) matrices PRECALCULUS - MATRICES scallywag 2 OF 4 . just now it can be single-minded without using intercellular substance propagation directly by using the Gaussian Elimination procedures .

number bingle , the matrices A and C atomic number 18 joined to form one increase matrix as such A serial of elementary courseing operations argon wherefore used to smother the matrix to the dustup echelon form This matrix is hence indite as three equations in conventional form The equations are then solved consecutive by substitution , head start by substituting the chousen apprise of z (third equation ) into the guerilla equation , solving for y , then substituting into the counterweight printing equation , then solving for x , submissive the 1993 , pp 543-553Before we foreshorten all of this work , it is important to determine if the dodging of equations has a ancestor , or has an infinite number of solutions . As an example of a dodging of equations that has no solution reckon this establishment of linear equations PRECALCULUS - MATRICES PAGE 3 OF 4Written in the augmented matrix form , this system isMultiply grade 1 by -2 and kick in it to wrangling 2Multiply row 1 by -2 and adjoin 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 pauperism to get a mount essay, order it on our website: Ordercustompaper.com

If you want to get a full essay, wisit our page: write my paper