algebra formulas
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Algebra
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http://course-notes.org/Algebra
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pythogorean theorem
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a^2 + b^2 = c^2
Systems Vocabulary
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inverse matrix method
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Inverse Matrix Method The inverse matrix method is a method of solving an unsolved system of equations by using a matrix and the formula AA=I and AX= B to find the solution to the variables where I is the identity matrix. Start with your unsolved linear system. You must make sure that you have an equal number of variables and equations or the method won?t work. Line the coefficients up in a matrix by system. For example, If your systems were: -1x + 1y + 3z = 2 -1 1 3 x 2 2 x + 1y +2z = 2 then you would arrange it as 2 1 2 y 2
Ap World Essay Outline Chapter 12
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Keith Coates 4th Essay 3.7 Compare and Contrast Essay Outline: Compare the social and religious elements of the Aztec and Inca empires. How might these elements help explain the successes experienced by these cultures? Thesis: The social and religious elements of the Aztec and Inca empires are extremely similar. For instance they both used the Mit?a system and appointed their leaders the same way. Aztecs were bigger in numbers but the Inca was bigger in culture and skill. They borrowed and learned many things from each other. Social Elements Virtually Same Mit?a One supreme ruler with other leaders under him Used khipus Ayllus Class divisions Loved their llamas Had the same needs for survival Llama herds Used ayllus Military very important to both civilizations Used Khipus
quadratic formula
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x equals negative b plus or minus the square root of b squared minus 4 ac all over 2 a
sing to tune of pop goes the weasel
Basic Algebraic Laws
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Commutative Law For Addition:
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a + b = b + a
ex. 5 + 7 = 7 + 5 =12
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Commutative Law For Multiplication:
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a x b = b x a
ex. 3 x 6 = 6 x 3 = 18
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Associative Law For Addition:
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(a + b) + c = a + (b + c)
ex. (4 + 6) + 5 = 4 + (6 + 5) = 15
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Associative Law For Multiplication:
Algebra and Equivalent
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ELEMENTARY LINEAR ALGEBRA K. R. MATTHEWS DEPARTMENT OF MATHEMATICS UNIVERSITY OF QUEENSLAND Corrected Version, 10th February 2010 Comments to the author at [email protected] Contents 1 LINEAR EQUATIONS 1 1.1 Introduction to linear equations . . . . . . . . . . . . . . . . . 1 1.2 Solving linear equations . . . . . . . . . . . . . . . . . . . . . 5 1.3 The Gauss?Jordan algorithm . . . . . . . . . . . . . . . . . . 8 1.4 Systematic solution of linear systems. . . . . . . . . . . . . . 9 1.5 Homogeneous systems . . . . . . . . . . . . . . . . . . . . . . 16 1.6 PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2 MATRICES 23 2.1 Matrix arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . 23
1wd
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APES Chapter 2 Vocab (Miller)
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