By ed van der Geer at al Birkhaeuser

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**Additional resources for Arithmetic Algebraic Geometry**

**Example text**

8 The greatest integer function, denoted by fix) = [x], is defined by fix) = j, where/ is the integer with the property that; & x

A function with the property that is an even function, while a function with the property P(-x) = -P(x) is an odd function. It would be possible to obtain the graph of a polynomial function y = P(x) by simply setting up a table and plotting a large number of points; this is how a computer or a graphing calculator operates. However, it is often desirable to have some basic information about the graph prior to plotting points. The graph of the polynomial function, y = a0 is a line which is parallel to the x-axis and | a0 \ units above or below the *-axis, depending on whether a0 is positive or negative.

Here is an example which illustrates the use of matrices to solve a system of two equations in two unknowns. EXAMPLE Solve the following system of equations using the inverse of a matrix. AC + y = 1 2x-y = 5 A= n i t -i 2 -1 2. _1 3 x=2 and 3 5 y=-I 34 The Method of Substitution The method of substitution uses one equation to solve for one variable in terms of the other. This variable is then substituted in the second equation to have one equation using one variable. Solve for this variable and then use it to obtain the other variable by virtue of the first equation.