2053Lecture2

# 12th algebra algebra algebra is the formal

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Unformatted text preview: the positional number system and the number zero to the Western world in the 12th century. 12th Algebra Algebra Algebra is the formal manipulation of symbols {a, b, c, …; 0, 1, 2,…} using an addition (+) a, and a multiplication (·), which satisfy the which following axioms: following Additive identity & inverse: a+0=a=0+a a + (– a ) = 0 = (– a ) + a Associativity : (a + b) + c = a + (b + c) Associativity Algebra, cont. Algebra, Multiplicative identity & inverse, a·1=a=1·a a · a–1 = 1 = a–1 · a Commutativity: a + b = b + a Commutativity: Distributivity: a · ( b + c) = a · b + a · c ( b + c) · a = b · a + c · a Simultaneous Equations Simultaneous One of the major applications of algebra is the One following: Given a system of equations, determine all the values of the variables which satisfy the system of equations. We can find all the solutions to the system of equations by using one of the following algebraic methods: one Directly, Kramer’s Rule, and Matrix method. Construction of Real Spaces Constructi...
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