19th Edition

ISBN: 9780998625720

Author: Lynn Marecek

Publisher: OpenStax College

Concept explainers

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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

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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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Textbook Question

Chapter 3.2, Problem 3.26TI

Find the slope of the line: y = 7 .

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Chapter 3.2, Problem 3.25TI

Chapter 3.2, Problem 3.27TI

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Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N then dim M = dim N but the converse need not to be true. B: Let A and B two balanced subsets of a linear space X, show that whether An B and AUB are balanced sets or nor verly A:LeLM be a subset of a linear space X, show that M is a hyperplane of X iff there exists fe X'/[0] and a EF such that M = {x Ex/f(x) = = a}. B:Show that every two norms on finite dimension linear space are equivalent C: Let f be a linear function from a normed space X in to a normed space Y, show that continuous at x, EX iff for any sequence (x) in X converge to x, then the sequence (f(x)) converge to (f(x)) in Y.

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Let & be linear map from as Pacex into aspace and {X1, X2, – 1— x3 basis for x show that f a one-to-one isf {f(x1), f (xx); — F (Kn) } linearly independent. மம் let M be a Proper sub space of aspace X then M is ahyper space iff for any text&M X=. C) let X be a linear space and fe X1{0} Show that is bjective or not and why? ***********

Chapter 3 Solutions

Intermediate Algebra

Ch. 3.1 - Plot each point in a rectangular coordinate system...Ch. 3.1 - Plot each point in a rectangular coordinate system...Ch. 3.1 - Use graph of y=3x1 . For each ordered pair,...Ch. 3.1 - Use graph of y=3x1 . For each ordered pair,...Ch. 3.1 - Graph the equation by plotting points: y=2x3 .Ch. 3.1 - Graph the equation by plotting points: y=2x+4 .Ch. 3.1 - Graph the equation: y=13x1 .Ch. 3.1 - Graph the equation: y=14x+2 .Ch. 3.1 - Graph the equations: (a) x=5 (b) y=4 .Ch. 3.1 - Graph the equations: (a) x=2 (b) y=3

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