Contemporary Abstract Algebra
Contemporary Abstract Algebra
9th Edition
ISBN: 9781305657960
Author: Joseph Gallian
Publisher: Cengage Learning
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Concept explainers

Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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Chapter 28, Problem 16E
To determine

To label the remaining points in the given figure in the form αiβj .

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In the following figure, there is a point labeled 1. Let α be the translationof the plane that carries the point labeled 1 to the point labeledα , and let β be the translation of the plane that carries thepoint labeled 1 to the point labeled b. The image of 1 under thecomposition of α and β is labeled α β. In the corresponding fashion,label the remaining points in the figure in the form α iβj.
Suppose P is the plane described by the equation ax+-by + cz + d = 0. Given two points (X0, Y0, Z0) and (x1,y1,z1), how does one go about determining whether or not the two points lie on the same side of the plane?
find the equation of the plane with the given description. Passes through O and is parallel to 4x − 9y + z = 3

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Contemporary Abstract Algebra

Ch. 28 - Prob. 16E
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