LC BEG & INT ALGEBRA
6th Edition
ISBN: 9781266315183
Author: Miller
Publisher: MCG
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Chapter 15.2, Problem 98PE
To determine
To Find: The measure of angles
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C=59(F−32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I onlyB) II onlyC) III onlyD) I and II only
(1) Let F be a field, show that the vector space F,NEZ* be a finite dimension.
(2) Let P2(x) be the vector space of polynomial of degree equal or less than two
and M={a+bx+cx²/a,b,cЄ R,a+b=c),show that whether Mis hyperspace or not.
(3) Let A and B be a subset of a vector space such that ACB, show that whether:
(a) if A is convex then B is convex or not. (b) if B is convex then A is convex or not.
(4) Let R be a field of real numbers and X=R, X is a vector space over R show that by
definition the norms/II.II, and II.112 on X are equivalent where
Ilxll₁ = max(lx,l, i=1,2,...,n) and llxll₂=(x²).
oper
(5) Let Ⓡ be a field of real numbers, Ⓡis a normed space under usual operations and
norm, let E=(2,5,8), find int(E), b(E) and D(E).
(6) Write the definition of bounded linear function between two normed spaces and
write with prove the relation between continuous and bounded linear function
between two normed spaces.
ind
→ 6
Q₁/(a) Let R be a field of real numbers and X-P(x)=(a+bx+cx²+dx/ a,b,c,dER},X is
a vector space over R, show that is finite dimension.
(b) Let be a bijective linear function from a finite dimension vector ✓ into
a space Yand Sbe a basis for X, show that whether f(S) basis for or not.
(c) Let be a vector space over a field F and A,B)affine subsets of X,show that
whether aAn BB, aAU BB be affine subsets of X or not, a,ẞ EF.
(12
Jal (answer only two) (6) Let M be a non-empty subset of a vector space X and tEX,
show that M is a hyperspace of X iff t+M is a hyperplane of X and tЄt+M.
(b) State Jahn-Banach theorem and write with prove an application of Hahn-
Chapter 15 Solutions
LC BEG & INT ALGEBRA
Ch. 15.1 - Prob. 1SPCh. 15.1 - Prob. 2SPCh. 15.1 - Prob. 3SPCh. 15.1 - Prob. 4SPCh. 15.1 - Prob. 5SPCh. 15.1 - Prob. 6SPCh. 15.1 - Prob. 7SPCh. 15.1 - Prob. 8SPCh. 15.1 - Prob. 9SPCh. 15.1 - Prob. 1PE
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- (b) Let A and B be two subset of a linear space X such that ACB, show that whether if A is affine set then B affine or need not and if B affine set then A affine set or need not. Qz/antonly be a-Show that every hyperspace of a vecor space X is hyperplane but the convers need not to be true. b- Let M be a finite dimension subspace of a Banach space X show that M is closed set. c-Show that every two norms on finite dimension vector space are equivant (1) Q/answer only two a-Write the definition of bounded set in: a normed space and write with prove an equivalent statement to a definition. b- Let f be a function from a normed space X into a normed space Y, show that f continuous iff f is bounded. c-Show that every finite dimension normed space is a Banach. Q/a- Let A and B two open sets in a normed space X, show that by definition AnB and AUB are open sets. (1 nood truearrow_forwardlog (6x+5)-log 3 = log 2 - log xarrow_forward1 The ratio of Argan to Potassium from a sample found sample found in Canada is .195 Find The estimated age of the sample A In (1+8.33 (+)) t = (1-26 × 109) en (1 In aarrow_forward
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- (1) Let M and N be non-empty subsets of a linear space X, show that whether = U or not, and show that there whether exsits a liear function from P₂(x) into R' which onto but not one-to-one or not. ام (2) Let R be a field of real numbers and P,(x)=(a+bx+cx? / a,b,ce R} be a vector space over R, show that whether there exsit two hyperspaces A and B such that AUB is a hyperspace or not. (3) Let A be an affine set in a linear space X over afield F and tEA, show that A-t is a subspace of Xand show that if M and N are balanced sets then M+N is balanced set. (4) Write the definition of bounded set in a normed space, and write with prove an equivalent statement to definition. (5) Let d be a metric on a linear space X over a field F, write conditions on d in order to get that there is a norm on X induced dy d and prove that. (6) Let M be a non-empty subset of a normed space X, show that xEcl(M) iff for any r>o there exsits yEM such that llx-yllarrow_forwardFind all solutions to the following equation. Do you get any extraneous solutions? Explain why or why not. 2 2 + x+1x-1 x21 Show all steps in your process. Be sure to state your claim, provide your evidence, and provide your reasoning before submitting.arrow_forwardDirections: For problems 1 through 3, read each question carefully and be sure to show all work. 1. What is the phase shift for y = 2sin(2x-)? 2. What is the amplitude of y = 7cos(2x+л)? 3. What is the period of y = sin(3x-π)? Directions: For problems 4 and 5, you were to compare and contrast the two functions in each problem situation. Be sure to include a discussion of similarities and differences for the periods, amplitudes, y-minimums, y-maximums, and any phase shift between the two graphs. Write in complete sentences. 4. y 3sin(2x) and y = 3cos(2x) 5. y 4sin(2x) and y = cos(3x- -플)arrow_forward2. Find the exact value of 12 + 12+12+√√12+ √12+ 12arrow_forwardTechnetium-99m is used as a radioactive tracer for certain medical tests. It has a half-life of 1 day. Consider the function TT where T(d)T(d) =100(2)−d=100(2)−d is the percent of Technetium-99m remaining dd days after the test. Which expression represents the number of days until only 5% remains?arrow_forward1. Find the inverse of f(x) = = 2x 1+2x Then find the domain of the inverse.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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