Beginning & Intermediate Algebra Plus NEW MyLab Math with Pearson eText -- Access Card Package (6th Edition)
6th Edition
ISBN: 9780134194004
Author: Elayn Martin-Gay
Publisher: PEARSON
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Chapter B.4, Problem 20E
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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
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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
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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.GYiff
Chapter B Solutions
Beginning & Intermediate Algebra Plus NEW MyLab Math with Pearson eText -- Access Card Package (6th Edition)
Ch. B.1 - Prob. 1PCh. B.1 - Prob. 2PCh. B.1 - Prob. 3PCh. B.1 - Prob. 4PCh. B.1 - Prob. 5PCh. B.1 - Prob. 1ECh. B.1 - Prob. 2ECh. B.1 - Prob. 3ECh. B.1 - Prob. 4ECh. B.1 - Prob. 5E
Ch. B.1 - Prob. 6ECh. B.1 - Prob. 7ECh. B.1 - Prob. 8ECh. B.1 - Prob. 9ECh. B.1 - Prob. 10ECh. B.1 - Prob. 11ECh. B.1 - Prob. 12ECh. B.1 - Prob. 13ECh. B.1 - Prob. 14ECh. B.1 - Prob. 15ECh. B.1 - Prob. 16ECh. B.1 - Prob. 17ECh. B.1 - Prob. 18ECh. B.1 - Prob. 19ECh. B.1 - Prob. 20ECh. B.1 - Prob. 21ECh. B.1 - Prob. 22ECh. B.1 - Prob. 23ECh. B.1 - Prob. 24ECh. B.1 - Prob. 25ECh. B.1 - Prob. 26ECh. B.1 - Prob. 27ECh. B.1 - Prob. 28ECh. B.1 - Prob. 29ECh. B.1 - Prob. 30ECh. B.1 - Prob. 31ECh. B.1 - Prob. 32ECh. B.1 - Prob. 33ECh. B.1 - Prob. 34ECh. B.1 - Prob. 35ECh. B.1 - Prob. 36ECh. B.1 - Prob. 37ECh. B.1 - Prob. 38ECh. B.1 - Prob. 39ECh. B.1 - Prob. 40ECh. B.1 - Prob. 41ECh. B.1 - Prob. 42ECh. B.1 - Prob. 43ECh. B.1 - Prob. 44ECh. B.1 - Prob. 45ECh. B.1 - Prob. 46ECh. B.1 - Prob. 47ECh. B.1 - Prob. 48ECh. B.1 - Prob. 49ECh. B.1 - Prob. 50ECh. B.1 - Prob. 51ECh. B.1 - Prob. 52ECh. B.1 - Prob. 53ECh. B.1 - Prob. 54ECh. B.1 - Prob. 55ECh. B.1 - Prob. 56ECh. B.2 - Prob. 1PCh. B.2 - Prob. 2PCh. B.2 - Prob. 3PCh. B.2 - Prob. 4PCh. B.2 - Prob. 1VCh. B.2 - Prob. 2VCh. B.2 - Prob. 3VCh. B.2 - Prob. 4VCh. B.2 - Prob. 5VCh. B.2 - Prob. 6VCh. B.2 - Prob. 7VCh. B.2 - Prob. 8VCh. B.2 - Prob. 9VCh. B.2 - Prob. 10VCh. B.2 - Prob. 11VCh. B.2 - Prob. 12VCh. B.2 - Prob. 1ECh. B.2 - Prob. 2ECh. B.2 - Prob. 3ECh. B.2 - Prob. 4ECh. B.2 - Prob. 5ECh. B.2 - Prob. 6ECh. B.2 - Prob. 7ECh. B.2 - Prob. 8ECh. B.2 - Prob. 9ECh. B.2 - Prob. 10ECh. B.2 - Prob. 11ECh. B.2 - Prob. 12ECh. B.2 - Prob. 13ECh. B.2 - Prob. 14ECh. B.2 - Prob. 15ECh. B.2 - Prob. 16ECh. B.2 - Prob. 17ECh. B.2 - Prob. 18ECh. B.2 - Prob. 19ECh. B.2 - Prob. 20ECh. B.2 - Prob. 21ECh. B.2 - Prob. 22ECh. B.2 - Prob. 23ECh. B.2 - Prob. 24ECh. B.2 - Prob. 25ECh. B.2 - Prob. 26ECh. B.2 - Prob. 27ECh. B.2 - Prob. 28ECh. B.2 - Prob. 29ECh. B.2 - Prob. 30ECh. B.2 - Prob. 31ECh. B.2 - Prob. 32ECh. B.2 - Prob. 33ECh. B.2 - Prob. 34ECh. B.2 - Prob. 35ECh. B.2 - Prob. 36ECh. B.2 - Prob. 37ECh. B.2 - Prob. 38ECh. B.2 - Prob. 39ECh. B.2 - Prob. 40ECh. B.2 - Prob. 41ECh. B.2 - Prob. 42ECh. B.2 - Prob. 43ECh. B.2 - Prob. 44ECh. B.2 - Prob. 45ECh. B.2 - Prob. 46ECh. B.2 - Prob. 47ECh. B.2 - Prob. 48ECh. B.2 - Prob. 49ECh. B.2 - Prob. 50ECh. B.2 - Prob. 51ECh. B.2 - Prob. 52ECh. B.2 - Prob. 53ECh. B.2 - Prob. 54ECh. B.2 - Prob. 55ECh. B.2 - Prob. 56ECh. B.2 - Prob. 57ECh. B.2 - Prob. 58ECh. B.2 - Prob. 59ECh. B.2 - Prob. 60ECh. B.2 - Prob. 61ECh. B.2 - Prob. 62ECh. B.2 - Prob. 63ECh. B.2 - Prob. 64ECh. B.2 - Prob. 65ECh. B.2 - Prob. 66ECh. B.3 - Prob. 1PCh. B.3 - Prob. 2PCh. B.3 - Prob. 3PCh. B.3 - Prob. 1ECh. B.3 - Prob. 2ECh. B.3 - Prob. 3ECh. B.3 - Prob. 4ECh. B.3 - Prob. 5ECh. B.3 - Prob. 6ECh. B.3 - Prob. 7ECh. B.3 - Prob. 8ECh. B.3 - Prob. 9ECh. B.3 - Prob. 10ECh. B.3 - Prob. 11ECh. B.3 - Prob. 12ECh. B.3 - Prob. 13ECh. B.3 - Prob. 14ECh. B.3 - Prob. 15ECh. B.3 - Prob. 16ECh. B.3 - Prob. 17ECh. B.3 - Prob. 18ECh. B.3 - Prob. 19ECh. B.3 - Prob. 20ECh. B.3 - Prob. 21ECh. B.3 - Prob. 22ECh. B.3 - Prob. 23ECh. B.3 - Prob. 24ECh. B.3 - Prob. 25ECh. B.3 - Prob. 26ECh. B.3 - Prob. 27ECh. B.3 - Prob. 28ECh. B.3 - Prob. 29ECh. B.3 - Prob. 30ECh. B.3 - Prob. 31ECh. B.3 - Prob. 32ECh. B.3 - Prob. 33ECh. B.3 - Prob. 34ECh. B.3 - Prob. 35ECh. B.3 - Prob. 36ECh. B.3 - Prob. 37ECh. B.3 - Prob. 38ECh. B.3 - Prob. 39ECh. B.3 - Prob. 40ECh. B.3 - Prob. 41ECh. B.3 - Prob. 42ECh. B.4 - Prob. 1PCh. B.4 - Prob. 2PCh. B.4 - Prob. 1ECh. B.4 - Prob. 2ECh. B.4 - Prob. 3ECh. B.4 - Prob. 4ECh. B.4 - Prob. 5ECh. B.4 - Prob. 6ECh. B.4 - Prob. 7ECh. B.4 - Prob. 8ECh. B.4 - Prob. 9ECh. B.4 - Prob. 10ECh. B.4 - Prob. 11ECh. B.4 - Prob. 12ECh. B.4 - Prob. 13ECh. B.4 - Prob. 14ECh. B.4 - Prob. 15ECh. B.4 - Prob. 16ECh. B.4 - Prob. 17ECh. B.4 - Prob. 18ECh. B.4 - Prob. 19ECh. B.4 - Prob. 20ECh. B.4 - Prob. 21ECh. B.4 - Prob. 22ECh. B.4 - Prob. 23ECh. B.4 - Prob. 24ECh. B.4 - Prob. 25ECh. B.4 - Prob. 26ECh. B.4 - Prob. 27ECh. B.4 - Prob. 28ECh. B.4 - Prob. 29ECh. B.4 - Prob. 30ECh. B.4 - Prob. 31ECh. B.4 - Prob. 32ECh. B.4 - Prob. 33ECh. B.4 - Prob. 34ECh. B.4 - Prob. 35ECh. B.4 - Prob. 36ECh. B.4 - Prob. 37ECh. B.4 - Prob. 38ECh. B.4 - Prob. 39ECh. B.4 - Prob. 40ECh. B.4 - Prob. 41ECh. B.4 - Prob. 42ECh. B.4 - Prob. 43ECh. B.4 - Prob. 44ECh. B.4 - Prob. 45ECh. B.4 - Prob. 46ECh. B.4 - Prob. 47ECh. B.4 - Prob. 48ECh. B.4 - Prob. 49ECh. B.4 - Prob. 50ECh. B.4 - Prob. 51ECh. B.4 - Prob. 52ECh. B.4 - Prob. 53ECh. B.4 - Prob. 54ECh. B.4 - Prob. 55ECh. B.4 - Prob. 56ECh. B.4 - Prob. 57ECh. B.5 - Prob. 1PCh. B.5 - Prob. 2PCh. B.5 - Prob. 3PCh. B.5 - Prob. 4PCh. B.5 - Prob. 1ECh. B.5 - Prob. 2ECh. B.5 - Prob. 3ECh. B.5 - Prob. 4ECh. B.5 - Prob. 5ECh. B.5 - Prob. 6ECh. B.5 - Prob. 7ECh. B.5 - Prob. 8ECh. B.5 - Prob. 9ECh. B.5 - Prob. 10ECh. B.5 - Prob. 11ECh. B.5 - Prob. 12ECh. B.5 - Prob. 13ECh. B.5 - Prob. 14ECh. B.5 - Prob. 15ECh. B.5 - Prob. 16ECh. B.5 - Prob. 17ECh. B.5 - Prob. 18ECh. B.5 - Prob. 19ECh. B.5 - Prob. 20ECh. B.5 - Prob. 21ECh. B.5 - Prob. 22ECh. B.5 - Prob. 23ECh. B.5 - Prob. 24ECh. B.5 - Prob. 25ECh. B.5 - Prob. 26ECh. B.5 - Prob. 27ECh. B.5 - Prob. 28ECh. B.5 - Prob. 29ECh. B.5 - Prob. 30ECh. B.5 - Prob. 31ECh. B.5 - Prob. 32ECh. B.5 - Prob. 33E
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