Prealgebra & Introductory Algebra (4th Edition)
4th Edition
ISBN: 9780321955791
Author: Elayn Martin-Gay
Publisher: PEARSON
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Chapter 14.1, Problem 20E
To determine
To find:
The solution of the system of linear equations by graphing.
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What is the domain and range, thank you !!
Assume a bivariate patch p(u, v) over the unit square [0, 1]² that is given as a tensor product patch where
u-sections (u fixed to some constant û; v varying across [0, 1]) are quadratic polynomials Pu:û(v) = p(û, v)
while v-sections are lines pv:ô (u) = p(u, v). The boundary lines pv:o(u) and pv:1 (u) are specified by their
end points p(0,0) 0.8 and p(1,0) 0.2 as well as p(0, 1) 0.3 and p(1, 1) = 0.8. The boundary
quadratics pu:o(v) and pu:1 (v) interpolate p(0,0.5) = 0.1 and p(1, 0.5) = 0.9 in addition to the above given
four corner-values.
=
=
=
Use Pu:û(v) = (1, v, v² ) Mq (Pu:û(0), Pu:û (0.5), Pu:û(1)) with
Ma
=
1 0 0
-3
4-1
2 4 2
(Pv:ô
as well as pu: (u) = (1, u) M₁ (pv:v (0), P: (1)) with
M₁
=
= (19)
0
to formulate p(u, v) using the "geometric input" G with
G
=
= (P(0,0%)
p(0,0) p(0,0.5) p(0,1)
) = ( 0.39
0.8 0.1 0.3
0.2 0.9 0.8
p(1,0) p(1, 0.5) p(1, 1)
See the figure below for (left) a selection of iso-lines of p(u, v) and (right) a 3D rendering of p(u, v) as a
height surface…
12. Suppose that a, b E R and a < b. Show that the vector space C[a, b] of all continuous complex
valued functions defined on [a, b], with supremum norm
is a Banach space.
Ilflloc:
=
sup f(t),
t€[a,b]
Chapter 14 Solutions
Prealgebra & Introductory Algebra (4th Edition)
Ch. 14.1 - Prob. 1PCh. 14.1 - Prob. 2PCh. 14.1 - Prob. 3PCh. 14.1 - Prob. 4PCh. 14.1 - Prob. 5PCh. 14.1 - Prob. 6PCh. 14.1 - Prob. 7PCh. 14.1 - Prob. 8PCh. 14.1 - Prob. 1VRVCCh. 14.1 - Prob. 2VRVC
Ch. 14.1 - Prob. 3VRVCCh. 14.1 - Prob. 4VRVCCh. 14.1 - Prob. 5VRVCCh. 14.1 - Prob. 6VRVCCh. 14.1 - Prob. 7VRVCCh. 14.1 - Prob. 8VRVCCh. 14.1 - Prob. 9VRVCCh. 14.1 - Prob. 10VRVCCh. 14.1 - Prob. 1ECh. 14.1 - Prob. 2ECh. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - Prob. 10ECh. 14.1 - Prob. 11ECh. 14.1 - Prob. 12ECh. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.1 - Prob. 16ECh. 14.1 - Prob. 17ECh. 14.1 - Prob. 18ECh. 14.1 - Prob. 19ECh. 14.1 - Prob. 20ECh. 14.1 - Prob. 21ECh. 14.1 - Prob. 22ECh. 14.1 - Prob. 23ECh. 14.1 - Prob. 24ECh. 14.1 - Prob. 25ECh. 14.1 - Prob. 26ECh. 14.1 - Prob. 27ECh. 14.1 - Prob. 28ECh. 14.1 - Prob. 29ECh. 14.1 - Prob. 30ECh. 14.1 - Prob. 31ECh. 14.1 - Prob. 32ECh. 14.1 - Prob. 33ECh. 14.1 - Prob. 34ECh. 14.1 - Prob. 35ECh. 14.1 - Prob. 36ECh. 14.1 - Prob. 37ECh. 14.1 - Prob. 38ECh. 14.1 - Prob. 39ECh. 14.1 - Prob. 40ECh. 14.1 - Prob. 41ECh. 14.1 - Prob. 42ECh. 14.1 - Prob. 43ECh. 14.1 - Prob. 44ECh. 14.1 - Prob. 45ECh. 14.1 - Prob. 46ECh. 14.1 - Prob. 47ECh. 14.1 - Prob. 48ECh. 14.1 - Prob. 49ECh. 14.1 - Prob. 50ECh. 14.1 - Prob. 51ECh. 14.1 - Prob. 52ECh. 14.1 - Prob. 53ECh. 14.1 - Prob. 54ECh. 14.1 - Prob. 55ECh. 14.1 - Prob. 56ECh. 14.1 - Prob. 57ECh. 14.1 - Prob. 58ECh. 14.1 - Prob. 59ECh. 14.1 - Prob. 60ECh. 14.1 - Prob. 61ECh. 14.1 - Prob. 62ECh. 14.1 - Prob. 63ECh. 14.1 - Prob. 64ECh. 14.1 - Prob. 65ECh. 14.1 - Prob. 66ECh. 14.1 - Prob. 67ECh. 14.1 - Prob. 68ECh. 14.1 - Prob. 69ECh. 14.1 - Prob. 70ECh. 14.1 - Prob. 71ECh. 14.1 - Prob. 72ECh. 14.1 - Prob. 1CECh. 14.1 - Prob. 2CECh. 14.1 - Prob. 3CECh. 14.1 - Prob. 4CECh. 14.2 - Prob. 1CCCh. 14.2 - Prob. 2CCCh. 14.2 - Prob. 3CCCh. 14.2 - Prob. 1PCh. 14.2 - Prob. 2PCh. 14.2 - Prob. 3PCh. 14.2 - Prob. 4PCh. 14.2 - Prob. 5PCh. 14.2 - Prob. 6PCh. 14.2 - Prob. 1VRVCCh. 14.2 - Prob. 2VRVCCh. 14.2 - Prob. 3VRVCCh. 14.2 - Prob. 4VRVCCh. 14.2 - Prob. 5VRVCCh. 14.2 - Prob. 6VRVCCh. 14.2 - Prob. 1ECh. 14.2 - 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Prob. 53ECh. 14.2 - Prob. 54ECh. 14.2 - Prob. 55ECh. 14.2 - Prob. 56ECh. 14.2 - Prob. 57ECh. 14.2 - Prob. 58ECh. 14.3 - Prob. 1CCCh. 14.3 - Prob. 2CCCh. 14.3 - Prob. 1PCh. 14.3 - Prob. 2PCh. 14.3 - Prob. 3PCh. 14.3 - Prob. 4PCh. 14.3 - Prob. 5PCh. 14.3 - Prob. 6PCh. 14.3 - Prob. 1VRVCCh. 14.3 - Prob. 2VRVCCh. 14.3 - Prob. 3VRVCCh. 14.3 - Prob. 4VRVCCh. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - Prob. 3ECh. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Prob. 7ECh. 14.3 - Prob. 8ECh. 14.3 - Prob. 9ECh. 14.3 - Prob. 10ECh. 14.3 - Prob. 11ECh. 14.3 - Prob. 12ECh. 14.3 - Prob. 13ECh. 14.3 - Prob. 14ECh. 14.3 - Prob. 15ECh. 14.3 - Prob. 16ECh. 14.3 - Prob. 17ECh. 14.3 - Prob. 18ECh. 14.3 - Prob. 19ECh. 14.3 - Prob. 20ECh. 14.3 - Prob. 21ECh. 14.3 - Prob. 22ECh. 14.3 - Prob. 23ECh. 14.3 - Prob. 24ECh. 14.3 - Prob. 25ECh. 14.3 - Prob. 26ECh. 14.3 - Prob. 27ECh. 14.3 - Prob. 28ECh. 14.3 - Prob. 29ECh. 14.3 - Prob. 30ECh. 14.3 - Prob. 31ECh. 14.3 - Prob. 32ECh. 14.3 - Prob. 33ECh. 14.3 - Prob. 34ECh. 14.3 - Prob. 35ECh. 14.3 - Prob. 36ECh. 14.3 - Prob. 37ECh. 14.3 - Prob. 38ECh. 14.3 - Prob. 39ECh. 14.3 - Prob. 40ECh. 14.3 - Prob. 41ECh. 14.3 - Prob. 42ECh. 14.3 - Prob. 43ECh. 14.3 - Prob. 44ECh. 14.3 - Prob. 45ECh. 14.3 - Prob. 46ECh. 14.3 - Prob. 47ECh. 14.3 - Prob. 48ECh. 14.3 - Prob. 49ECh. 14.3 - Prob. 50ECh. 14.3 - Prob. 51ECh. 14.3 - Prob. 52ECh. 14.3 - Prob. 53ECh. 14.3 - Prob. 54ECh. 14.3 - Prob. 55ECh. 14.3 - Prob. 56ECh. 14.3 - Prob. 57ECh. 14.3 - Prob. 58ECh. 14.3 - Prob. 59ECh. 14.3 - Prob. 60ECh. 14.IR - Prob. 1IRCh. 14.IR - Prob. 2IRCh. 14.IR - Prob. 3IRCh. 14.IR - Prob. 4IRCh. 14.IR - Prob. 5IRCh. 14.IR - Prob. 6IRCh. 14.IR - Prob. 7IRCh. 14.IR - Prob. 8IRCh. 14.IR - Prob. 9IRCh. 14.IR - Prob. 10IRCh. 14.IR - Prob. 11IRCh. 14.IR - Prob. 12IRCh. 14.IR - Prob. 13IRCh. 14.IR - Prob. 14IRCh. 14.IR - Prob. 15IRCh. 14.IR - Prob. 16IRCh. 14.IR - Prob. 17IRCh. 14.IR - Prob. 18IRCh. 14.IR - Prob. 19IRCh. 14.IR - Prob. 20IRCh. 14.IR - Prob. 21IRCh. 14.IR - Prob. 22IRCh. 14.4 - Prob. 1CCCh. 14.4 - Prob. 1PCh. 14.4 - Prob. 2PCh. 14.4 - Prob. 3PCh. 14.4 - Prob. 4PCh. 14.4 - Prob. 1ECh. 14.4 - Prob. 2ECh. 14.4 - Prob. 3ECh. 14.4 - Prob. 4ECh. 14.4 - Prob. 5ECh. 14.4 - Prob. 6ECh. 14.4 - Prob. 7ECh. 14.4 - Prob. 8ECh. 14.4 - Prob. 9ECh. 14.4 - Prob. 10ECh. 14.4 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Prob. 15ECh. 14.4 - Prob. 16ECh. 14.4 - Prob. 17ECh. 14.4 - Prob. 18ECh. 14.4 - Prob. 19ECh. 14.4 - Prob. 20ECh. 14.4 - Prob. 21ECh. 14.4 - Prob. 22ECh. 14.4 - Prob. 23ECh. 14.4 - Prob. 24ECh. 14.4 - Prob. 25ECh. 14.4 - Prob. 26ECh. 14.4 - Prob. 27ECh. 14.4 - Prob. 28ECh. 14.4 - Prob. 29ECh. 14.4 - Prob. 30ECh. 14.4 - Prob. 31ECh. 14.4 - Prob. 32ECh. 14.4 - Prob. 33ECh. 14.4 - Prob. 34ECh. 14.4 - Prob. 35ECh. 14.4 - Prob. 36ECh. 14.4 - Prob. 37ECh. 14.4 - Prob. 38ECh. 14.4 - Prob. 39ECh. 14.4 - Prob. 40ECh. 14.4 - Prob. 41ECh. 14.4 - Prob. 42ECh. 14.4 - Prob. 43ECh. 14.4 - Prob. 44ECh. 14.4 - Prob. 45ECh. 14.4 - Prob. 46ECh. 14.4 - Prob. 47ECh. 14.4 - Prob. 48ECh. 14.4 - Prob. 49ECh. 14.4 - Prob. 50ECh. 14.4 - Prob. 51ECh. 14.4 - Prob. 52ECh. 14.4 - Prob. 53ECh. 14.4 - Prob. 54ECh. 14.4 - Prob. 55ECh. 14.4 - Prob. 56ECh. 14.GA - Prob. 1GACh. 14.VC - Prob. 1VCCh. 14.VC - Prob. 2VCCh. 14.VC - Prob. 3VCCh. 14.VC - Prob. 4VCCh. 14.VC - Prob. 5VCCh. 14.VC - Prob. 6VCCh. 14.VC - Prob. 7VCCh. 14.CR - Prob. 1CRCh. 14.CR - Prob. 2CRCh. 14.CR - Prob. 3CRCh. 14.CR - Prob. 4CRCh. 14.CR - Prob. 5CRCh. 14.CR - Prob. 6CRCh. 14.CR - Prob. 7CRCh. 14.CR - Prob. 8CRCh. 14.CR - Prob. 9CRCh. 14.CR - Prob. 10CRCh. 14.CR - Prob. 11CRCh. 14.CR - Prob. 12CRCh. 14.CR - Prob. 13CRCh. 14.CR - Prob. 14CRCh. 14.CR - Prob. 15CRCh. 14.CR - Prob. 16CRCh. 14.CR - Prob. 17CRCh. 14.CR - Prob. 18CRCh. 14.CR - Prob. 19CRCh. 14.CR - Prob. 20CRCh. 14.CR - Prob. 21CRCh. 14.CR - Prob. 22CRCh. 14.CR - Prob. 23CRCh. 14.CR - Prob. 24CRCh. 14.CR - Prob. 25CRCh. 14.CR - Prob. 26CRCh. 14.CR - Prob. 27CRCh. 14.CR - Prob. 28CRCh. 14.CR - Prob. 29CRCh. 14.CR - Prob. 30CRCh. 14.CR - Prob. 31CRCh. 14.CR - Prob. 32CRCh. 14.CR - Prob. 33CRCh. 14.CR - Prob. 34CRCh. 14.CR - Prob. 35CRCh. 14.CR - Prob. 36CRCh. 14.CR - Prob. 37CRCh. 14.CR - Prob. 38CRCh. 14.CR - Prob. 39CRCh. 14.CR - Prob. 40CRCh. 14.CR - Prob. 41CRCh. 14.CR - Prob. 42CRCh. 14.CR - Prob. 43CRCh. 14.CR - Prob. 44CRCh. 14.CR - Prob. 45CRCh. 14.CR - Prob. 46CRCh. 14.CR - Prob. 47CRCh. 14.CR - Prob. 48CRCh. 14.CR - Prob. 49CRCh. 14.CR - Prob. 50CRCh. 14.CT - Prob. 1CTCh. 14.CT - Prob. 2CTCh. 14.CT - Prob. 3CTCh. 14.CT - Prob. 4CTCh. 14.CT - Prob. 5CTCh. 14.CT - Prob. 6CTCh. 14.CT - Prob. 7CTCh. 14.CT - Prob. 8CTCh. 14.CT - Prob. 9CTCh. 14.CT - Prob. 10CTCh. 14.CT - Prob. 11CTCh. 14.CT - Prob. 12CTCh. 14.CT - Prob. 13CTCh. 14.CT - Prob. 14CTCh. 14.CT - Prob. 15CTCh. 14.CT - Prob. 16CTCh. 14.CT - Prob. 17CTCh. 14.CT - Prob. 18CTCh. 14.CT - Prob. 19CTCh. 14.CT - Prob. 20CTCh. 14.CT - Prob. 21CTCh. 14.CT - Prob. 22CTCh. 14.CT - Prob. 23CTCh. 14.CT - Prob. 24CTCh. 14.CM - Prob. 1CMCh. 14.CM - Prob. 2CMCh. 14.CM - 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