The purpose of this collection of algebraic references is to provide a brief, clear and handy guide to the more important, formal rules of algebra and the most commonly used formulas for evaluating quantities, as well as examples of their applications for solving algebraic problems.
This section contains the following:
Fundamentals of Algebra,
Determinants
Linear Equations
Quadratic Equations
Inequalities
Sequences and Series
Functions and Their Graphs
The set of all rational numbers combined with the set of all irrational numbers gives us the set of real numbers. The relationships among the various sets of real numbers are shown below.
If a, b, and c are real numbers, then
Addition properties
| Commutative: | a + b = b + a |
| Associative: | ( a + b + c = a+( b + c) |
| Identity: | a+0=0 + a = a |
| Inverse: | a+(- a)=(- a) + a = 0 |
Multiplication properties
| Commutative: | ab = ba |
| Associative: | ( ab) c = a( bc) |
| Identity: | ( a 1=1 a = a |
| Inverse: | |
| Distributive: | a( b + c) = ab + ac |
If a, b, and c are real numbers, then
| Identity: | a = a |
| Symmetric: | If a = b, then b = a |
| Transitive: | If a = b |
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