EP COLLEGE ALGEBRA W/MODELING...-MYMATH
6th Edition
ISBN: 9780134418117
Author: Rockswold
Publisher: PEARSON CO
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Chapter R6, Problem 2E
Find the square roots of the number. Approximate your answers to the nearest hundredth whenever appropriate.
2. 49
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Which statement is true about the graph of the equation y = csc¯¹(x)?
There is a horizontal asymptote at y = 0.
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There is a horizontal asymptote at y = 2.
There is a vertical asymptote at x = 0.
O There is a vertical asymptote at x=-
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ے ملزمة احمد
Q (a) Let f be a linear map from a space X into a space Y and (X1,X2,...,xn) basis for X, show that fis one-to-
one iff (f(x1),f(x2),...,f(x) } linearly independent.
(b) Let X= {ao+ax₁+a2x2+...+anxn, a;ER} be a vector space over R, write with prove a hyperspace and a
hyperplane of X.
مبر خد احمد
Q₂ (a) Let M be a subspace of a vector space X, and A= {fex/ f(x)=0, x E M ), show that whether A is
convex set or not, affine set or not.
Write with prove an
application of Hahn-Banach theorem.
Show that every singleton set in a normed space X is closed and any finite set in X is closed (14M)
Let M be a proper subspace of a finite dimension vector space X over a field F show that
whether: (1) If S is a base for M then S base for X or not, (2) If T base for X then base for M
or not.
(b) Let X-P₂(x) be a vector space over polynomials a field of real numbers R, write with L
prove convex subset of X and hyperspace of X.
Q₂/ (a) Let X-R³ be a vector space over a over a field of real numbers R and
A=((a,b,o), a,bE R), A is a subspace of X, let g be a function from A into R such that
gla,b,o)-a, gEA, find fe X such that g(t)=f(t), tEA.
(b) Let M be a non-empty subset of a space X, show that M is a hyperplane of X iff there
Xiff there
exists fE X/10) and tE F such that M=(xE X/ f(x)=t).
(c) Show that the relation equivalent is an equivalence relation on set of norms on a space
X.
Chapter R6 Solutions
EP COLLEGE ALGEBRA W/MODELING...-MYMATH
Ch. R6 - Prob. 1ECh. R6 - Find the square roots of the number. Approximate...Ch. R6 - Find the square roots of the number. Approximate...Ch. R6 - Prob. 4ECh. R6 - Prob. 5ECh. R6 - Prob. 6ECh. R6 - Prob. 7ECh. R6 - Prob. 8ECh. R6 - Prob. 9ECh. R6 - Prob. 10E
Ch. R6 - Prob. 11ECh. R6 - Prob. 12ECh. R6 - Prob. 13ECh. R6 - Prob. 14ECh. R6 - Prob. 15ECh. R6 - Prob. 16ECh. R6 - Prob. 17ECh. R6 - Prob. 18ECh. R6 - Prob. 19ECh. R6 - Prob. 20ECh. R6 - Prob. 21ECh. R6 - Prob. 22ECh. R6 - Prob. 23ECh. R6 - Prob. 24ECh. R6 - Prob. 25ECh. R6 - Prob. 26ECh. R6 - Prob. 27ECh. R6 - Prob. 28ECh. R6 - Prob. 29ECh. R6 - Prob. 30ECh. R6 - Prob. 31ECh. R6 - Prob. 32ECh. R6 - Prob. 33ECh. R6 - Prob. 34ECh. R6 - Prob. 35ECh. R6 - Prob. 36ECh. R6 - Prob. 37ECh. R6 - Prob. 38ECh. R6 - Prob. 39ECh. R6 - Prob. 40ECh. R6 - Prob. 41ECh. R6 - Prob. 42ECh. R6 - Prob. 43ECh. R6 - Prob. 44ECh. R6 - Prob. 45ECh. R6 - Prob. 46ECh. R6 - Prob. 47ECh. R6 - Prob. 48ECh. R6 - Prob. 49ECh. R6 - Prob. 50ECh. R6 - Prob. 51ECh. R6 - Prob. 52ECh. R6 - Prob. 53ECh. R6 - Prob. 54ECh. R6 - Prob. 55ECh. R6 - Prob. 56ECh. R6 - Prob. 57ECh. R6 - Prob. 58ECh. R6 - Prob. 59ECh. R6 - Prob. 60ECh. R6 - Prob. 61ECh. R6 - Prob. 62ECh. R6 - Prob. 63ECh. R6 - Prob. 64ECh. R6 - Prob. 65ECh. R6 - Prob. 66ECh. R6 - Prob. 67ECh. R6 - Prob. 68ECh. R6 - Prob. 69ECh. R6 - Prob. 70ECh. R6 - Prob. 71ECh. R6 - Prob. 72ECh. R6 - Prob. 73ECh. R6 - Prob. 74ECh. R6 - Prob. 75ECh. R6 - Prob. 76ECh. R6 - Prob. 77ECh. R6 - Prob. 78ECh. R6 - Prob. 79ECh. R6 - Prob. 80ECh. R6 - Prob. 81ECh. R6 - Prob. 82ECh. R6 - Prob. 83ECh. R6 - Prob. 84ECh. R6 - Prob. 85ECh. R6 - Prob. 86ECh. R6 - Prob. 87ECh. R6 - Prob. 88ECh. R6 - Prob. 89ECh. R6 - Prob. 90ECh. R6 - Prob. 91ECh. R6 - Prob. 92ECh. R6 - Prob. 93ECh. R6 - Prob. 94ECh. R6 - Prob. 95ECh. R6 - Prob. 96ECh. R6 - Prob. 97ECh. R6 - Prob. 98ECh. R6 - Prob. 99ECh. R6 - Prob. 100ECh. R6 - Prob. 101ECh. R6 - Prob. 102ECh. R6 - Prob. 103ECh. R6 - Prob. 104ECh. R6 - Prob. 105ECh. R6 - Prob. 106ECh. R6 - Prob. 107ECh. R6 - Prob. 108ECh. R6 - Prob. 109ECh. R6 - Prob. 110ECh. R6 - Prob. 111ECh. R6 - Prob. 112ECh. R6 - Prob. 113ECh. R6 - Prob. 114ECh. R6 - Prob. 115ECh. R6 - Prob. 116ECh. R6 - Prob. 117ECh. R6 - Prob. 118ECh. R6 - Prob. 119ECh. R6 - Prob. 120ECh. R6 - Prob. 121ECh. R6 - Prob. 122E
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- Q/(a)Let X be a finite dimension vector space over a field F and S₁,S2CX such that S₁SS2. Show that whether (1) if S, is a base for X then base for X or not (2) if S2 is a base for X then S, is a base for X or not (b) Show that every subspace of vector space is convex and affine set but the conevrse need not to be true. allet M be a non-empty subset of a vector space X over a field F and x,EX. Show that M is a hyperspace iff xo+ M is a hyperplane and xo€ xo+M. bState Hahn-Banach theorem and write with prove an application about it. Show that every singleten subset and finite subset of a normed space is closed. Oxfallet f he a function from a normad roace YI Show tha ir continuour aty.GYiffarrow_forward7 3 2 x+11x+24 9 2 5 x+11x+24arrow_forward2 4 + 4x 2x 8 || 12arrow_forward
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