Transcription of ELEMENTARY LINEAR ALGEBRA - Number theory
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ELEMENTARYLINEAR ALGEBRAK. R. MATTHEWSDEPARTMENT OF MATHEMATICSUNIVERSITY OF QUEENSLANDC orrected Version, 27th April2013 Comments to the author at 1 LINEAR Introduction to LINEAR equationsAlinear equationinnunknownsx1, x2, , xnis an equation of the forma1x1+a2x2+ +anxn=b,wherea1, a2, .. , an, bare given real example, withxandyinstead ofx1andx2, the LINEAR equation2x+ 3y= 6 describes the line passing through the points (3,0) and (0,2).Similarly, withx, yandzinstead ofx1, x2andx3, the LINEAR equa-tion 2x+ 3y+ 4z= 12 describes the plane passing through the points(6,0,0),(0,4,0),(0,0,3).Asystemofm LINEAR equations innunknownsx1, x2, , xnis a familyof LINEAR equationsa11x1+a12x2+ +a1nxn=b1a21x1+a22x2+ +a2nxn= +am2x2+ +amnxn= wish to determine if such a system has a solution, that is tofindout if there exist numbersx1, x2, , xnwhich satisfy each of the equationssimultaneously.
ELEMENTARY LINEAR ALGEBRA K. R. MATTHEWS DEPARTMENT OF MATHEMATICS UNIVERSITY OF QUEENSLAND Corrected Version, 27th April 2013 Comments to the author at keithmatt@gmail.com
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250 PROBLEMS IN ELEMENTARY NUMBER, 250 problems in elementary number theory, Three–dimensional, Number theory, Galois theory, Theory, Teach Probability in the Elementary Classroom, Using manipulatives to teach elementary, Brief Review of Elementary Quantum Chemistry, Ludwig von Bertalanffy, ELEMENTARY