EBK LINEAR ALGEBRA AND ITS APPLICATIONS
6th Edition
ISBN: 9780135851043
Author: Lay
Publisher: PEARSON CO
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Chapter 4.8, Problem 3E
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The Course Name Real Analysis please Solve questions by Real Analysis
part 3 of the question is:
A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes.
What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model.
Will the last passenger to board the ride need to wait in order to exit the ride? Explain.
2. The duration of the ride is 15 min.
(a) How many times does the last passenger who boarded the ride make a complete loop on the Ferris
wheel?
(b) What is the position of that passenger when the ride ends?
Chapter 4 Solutions
EBK LINEAR ALGEBRA AND ITS APPLICATIONS
Ch. 4.1 - Show that the set H of all points in 2 of the form...Ch. 4.1 - Let W = Span{v1,...,vp}, where v1,..,vp are in a...Ch. 4.1 - An n n matrix A is said to be symmetric if AT =...Ch. 4.1 - Let V be the first quadrant in the xy-plane; that...Ch. 4.1 - Let W be the union of the first and third...Ch. 4.1 - Let H be the set of points inside and on the unit...Ch. 4.1 - Construct a geometric figure that illustrates why...Ch. 4.1 - In Exercises 58, determine if the given set is a...Ch. 4.1 - In Exercises 58, determine if the given set is a...Ch. 4.1 - In Exercises 58, determine if the given set is a...
Ch. 4.1 - In Exercises 58, determine if the given set is a...Ch. 4.1 - Let H be the set of all vectors of the form...Ch. 4.1 - Let H be the set of all vectors of the form...Ch. 4.1 - Let W be the set of all vectors of the form...Ch. 4.1 - Let W be the set of all vectors of the form...Ch. 4.1 - Let v1 = [101], v2 = [213], v3 = [426], and w=...Ch. 4.1 - Let v1, v2, v3 be as in Exercise 13, and let w =...Ch. 4.1 - In Exercises 1518, let W be the set of all vectors...Ch. 4.1 - In Exercises 1518, let W be the set of all vectors...Ch. 4.1 - In Exercises 1518, let W be the set of all vectors...Ch. 4.1 - In Exercises 1518, let W be the set of all vectors...Ch. 4.1 - If a mass m is placed at the end of a spring, and...Ch. 4.1 - The set of all continuous real-valued functions...Ch. 4.1 - Determine if the set H of all matrices of the form...Ch. 4.1 - Let F be a fixed 32 matrix, and let H be the set...Ch. 4.1 - Prob. 24ECh. 4.1 - In Exercises 23—32, mark each statement True or...Ch. 4.1 - In Exercises 23—32, mark each statement True or...Ch. 4.1 - In Exercises 23—32, mark each statement True or...Ch. 4.1 - In Exercises 23—32, mark each statement True or...Ch. 4.1 - In Exercises 23—32, mark each statement True or...Ch. 4.1 - Prob. 32ECh. 4.1 - Exercises 2529 show how the axioms for a vector...Ch. 4.1 - Exercises 2529 show how the axioms for a vector...Ch. 4.1 - Exercises 2529 show how the axioms for a vector...Ch. 4.1 - Exercises 2529 show how the axioms for a vector...Ch. 4.1 - Suppose cu = 0 for some nonzero scalar c. Show...Ch. 4.1 - Let u and v be vectors in a vector space V, and...Ch. 4.1 - Let H and K be sub spaces of a vector space V. The...Ch. 4.1 - Given subspaces H and K of a vector space V, the...Ch. 4.1 - Suppose u1,..., up and v1,..., vq are vectors in a...Ch. 4.1 - [M] Show that w is in the subspace of 4 spanned by...Ch. 4.1 - [M] Determine if y is in the subspace of 4 spanned...Ch. 4.1 - [M] The vector space H = Span {1, cos2t, cos4t,...Ch. 4.2 - Let W = {[abc]:a3bc=0}. Show in two different ways...Ch. 4.2 - Let A = [735415524], v = [211], and w = [763]....Ch. 4.2 - Let A be an n n matrix. If Col A = Nul A, show...Ch. 4.2 - Determine if w = [134] is in Nul A, where A =...Ch. 4.2 - Determine if w = [532] is in Nul A, where A =...Ch. 4.2 - In Exercises 36, find an explicit description of...Ch. 4.2 - In Exercises 36, find an explicit description of...Ch. 4.2 - In Exercises 36, find an explicit description of...Ch. 4.2 - In Exercises 36, find an explicit description of...Ch. 4.2 - In Exercises 714, either use an appropriate...Ch. 4.2 - In Exercises 714, either use an appropriate...Ch. 4.2 - In Exercises 714, either use an appropriate...Ch. 4.2 - In Exercises 714, either use an appropriate...Ch. 4.2 - In Exercises 714, either use an appropriate...Ch. 4.2 - In Exercises 714, either use an appropriate...Ch. 4.2 - In Exercises 714, either use an appropriate...Ch. 4.2 - In Exercises 714, either use an appropriate...Ch. 4.2 - In Exercises 15 and 16, find A such that the given...Ch. 4.2 - Prob. 16ECh. 4.2 - For the matrices in Exercises 1720, (a) find k...Ch. 4.2 - For the matrices in Exercises 1720, (a) find k...Ch. 4.2 - For the matrices in Exercises 1720, (a) find k...Ch. 4.2 - For the matrices in Exercises 17-20, (a) find k...Ch. 4.2 - With A as in Exercise 17, find a nonzero vector in...Ch. 4.2 - With A as in Exercise 3, find a nonzero vector in...Ch. 4.2 - Let A=[61236] and w=[21]. Determine if w is in Col...Ch. 4.2 - Let A=[829648404] and w=[212]. Determine w is in...Ch. 4.2 - In Exercises 25—38, A denotes an mn matrix. Mark...Ch. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - In Exercises 25—38, A denotes an mn matrix. Mark...Ch. 4.2 - Prob. 35ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - It can be shown that a solution of the system...Ch. 4.2 - Consider the following two systems of equations:...Ch. 4.2 - Prove Theorem 3 as follows: Given an m n matrix...Ch. 4.2 - Let T : V W be a linear transformation from a...Ch. 4.2 - Define T : p2 by T(p)=[p(0)p(1)]. For instance, if...Ch. 4.2 - Define a linear transformation T: p2 2 by...Ch. 4.2 - Let M22 be the vector space of all 2 2 matrices,...Ch. 4.2 - (Calculus required) Define T : C[0, 1 ] C[0, 1]...Ch. 4.2 - Let V and W be vector spaces, and let T : V W be...Ch. 4.2 - [M] Determine whether w is in the column space of...Ch. 4.2 - [M] Determine whether w is in the column space of...Ch. 4.2 - [M] Let a1,,a5 denote the columns of the matrix A,...Ch. 4.2 - [M] Let H = Span {v1, v2} and K = Span {v3, v4},...Ch. 4.3 - Let v1=[123] and v2=[279]. Determine if {v1, v2}...Ch. 4.3 - Let v1=[134], v2=[621], v3=[223], and v4=[489]....Ch. 4.3 - Let v1=[100], v2=[010], and H={[ss0]:sin}. Then...Ch. 4.3 - Let V and W be vector spaces, let T : V W and U :...Ch. 4.3 - Determine which sets in Exercises 1-8 are bases...Ch. 4.3 - Determine which sets in Exercises 1-8 are bases...Ch. 4.3 - Determine which sets in Exercises 1-8 are bases...Ch. 4.3 - Determine which sets in Exercises 1-8 are bases...Ch. 4.3 - Determine which sets in Exercises 1-8 are bases...Ch. 4.3 - Determine which sets in Exercises 1-8 are bases...Ch. 4.3 - Determine which sets in Exercises 1-8 are bases...Ch. 4.3 - Determine which sets in Exercises 1-8 are bases...Ch. 4.3 - Find bases for the null spaces of the matrices...Ch. 4.3 - Find bases for the null spaces of the matrices...Ch. 4.3 - Find a basis for the set of vectors in 3 in the...Ch. 4.3 - Find a basis for the set of vectors in 2 on the...Ch. 4.3 - In Exercises 13 and 14, assume that A is row...Ch. 4.3 - In Exercises 13 and 14, assume that A is row...Ch. 4.3 - In Exercises 15-18, find a basis for the space...Ch. 4.3 - In Exercises 15-18, find a basis for the space...Ch. 4.3 - In Exercises 15-18, find a basis for the space...Ch. 4.3 - In Exercises 15-18, find a basis for the space...Ch. 4.3 - Let v1=[437], v2=[192], v3=[7116], and H =...Ch. 4.3 - Let v1=[7495], v2=[4725], v3=[1534]. It can be...Ch. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - Suppose 4 = Span {v1,,v4}. Explain why {v1,,v4} is...Ch. 4.3 - Let B = {v1,..., vn} be a linearly independent set...Ch. 4.3 - Let v1=[101], v2=[011], v3=[010], and let H be the...Ch. 4.3 - In the vector space of all real-valued functions,...Ch. 4.3 - Let V be the vector space of functions that...Ch. 4.3 - (RLC circuit) The circuit in the figure consists...Ch. 4.3 - Exercises 29 and 30 show that every basis for n...Ch. 4.3 - Exercises 29 and 30 show that every basis for n...Ch. 4.3 - Exercises 31 and 32 reveal an important connection...Ch. 4.3 - Exercises 31 and 32 reveal an important connection...Ch. 4.3 - Consider the polynomials p1(t) = 1 + t2 and p2(t)...Ch. 4.3 - Consider the polynomials p1(t) = 1 + t, p2(t) = 1 ...Ch. 4.3 - Let V be a vector space that contains a linearly...Ch. 4.3 - [M] Let H = Span {u1, u2, u3} and K = Span{v1,v2,...Ch. 4.3 - [M] Show that {t, sin t, cos 2t, sin t cos t} is a...Ch. 4.4 - Let b1=[100], b2=[340], b3=[363], and x=[823]. a....Ch. 4.4 - The set B = {1 + t, 1 + t2, t + t2} is a basis for...Ch. 4.4 - In Exercises 1-4, find the vector x determined by...Ch. 4.4 - In Exercises 1-4, find the vector x determined by...Ch. 4.4 - In Exercises 1-4, find the vector x determined by...Ch. 4.4 - In Exercises 1-4, find the vector x determined by...Ch. 4.4 - In Exercises 5-8, find the coordinate vector [ x...Ch. 4.4 - In Exercises 5-8, find the coordinate vector [ x...Ch. 4.4 - In Exercises 5-8, find the coordinate vector [ x...Ch. 4.4 - In Exercises 5-8, find the coordinate vector [ x...Ch. 4.4 - In Exercises 9 and 10, find the...Ch. 4.4 - In Exercises 9 and 10, find the...Ch. 4.4 - In Exercises 11 and 12, use an inverse matrix to...Ch. 4.4 - In Exercises 11 and 12, use an inverse matrix to...Ch. 4.4 - The set B = {1 + t2, t + t2, 1 + 2t + t2} is a...Ch. 4.4 - The set B = {1 t2, t t2, 2 2t + t2} is a basis...Ch. 4.4 - Prob. 15ECh. 4.4 - The vectors v1=[13], v2=[28], v3=[37] span 2 but...Ch. 4.4 - Let B = {b1,...,bn} be a basis for a vector space...Ch. 4.4 - Let S be a finite set in a vector space V with the...Ch. 4.4 - Suppose {v1,...,v4} is a linearly dependent...Ch. 4.4 - Let B={[14],[29]}. Since the coordinate mapping...Ch. 4.4 - Exercises 23-26 concern a vector space V, a basis...Ch. 4.4 - Exercises 23-26 concern a vector space V, a basis...Ch. 4.4 - Exercises 23-26 concern a vector space V, a basis...Ch. 4.4 - Exercises 23-26 concern a vector space V, a basis...Ch. 4.4 - In Exercises 27-30, use coordinate vectors to test...Ch. 4.4 - In Exercises 27-30, use coordinate vectors to test...Ch. 4.4 - In Exercises 27-30, use coordinate vectors to test...Ch. 4.4 - In Exercises 27-30, use coordinate vectors to test...Ch. 4.4 - Use coordinate vectors to test whether the...Ch. 4.4 - Let p1 (t) = 1 + t2, p2(t) = t 3t2, p3 (t) = 1 +...Ch. 4.4 - In Exercises 33 and 34, determine whether the sets...Ch. 4.4 - In Exercises 33 and 34, determine whether the sets...Ch. 4.4 - Prob. 39ECh. 4.4 - [M] Let H = Span{v1,v2, v3} and B ={v1,v2, v3}....Ch. 4.4 - [M] Exercises 37 and 38 concern the crystal...Ch. 4.4 - [M] Exercises 37 and 38 concern the crystal...Ch. 4.5 - Decide whether each statement is True or False,...Ch. 4.5 - Let H and K be subspaces of a vector space V. In...Ch. 4.5 - For each subspace in Exercises 1-8, (a) find a...Ch. 4.5 - For each subspace in Exercises 1-8, (a) find a...Ch. 4.5 - For each subspace in Exercises 1-8, (a) find a...Ch. 4.5 - For each subspace in Exercises 1-8, (a) find a...Ch. 4.5 - For each subspace in Exercises 1-8, (a) find a...Ch. 4.5 - For each subspace in Exercises 1-8, (a) find a...Ch. 4.5 - For each subspace in Exercises 1-8, (a) find a...Ch. 4.5 - For each subspace in Exercises 1-8, (a) find a...Ch. 4.5 - In Exercises 11 and 12, find the dimension of the...Ch. 4.5 - In Exercises 11 and 12, find the dimension of the...Ch. 4.5 - Determine the dimensions of Nul A and Col A for...Ch. 4.5 - Determine the dimensions of Nul A and Col A for...Ch. 4.5 - Determine the dimensions of Nul A and Col A for...Ch. 4.5 - Determine the dimensions of Nul A and Col A for...Ch. 4.5 - Determine the dimensions of Nul A, Col A, and Row...Ch. 4.5 - Determine the dimensions of Nul A and Col A for...Ch. 4.5 - In Exercises 17—26, V is a vector space and A is...Ch. 4.5 - Prob. 18ECh. 4.5 - Prob. 22ECh. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - The first four Hermite polynomials are 1, 2t, 2 +...Ch. 4.5 - The first four Laguerre polynomials are 1, 1 t, 2...Ch. 4.5 - Let B be the basis of 3 consisting of the Hermite...Ch. 4.5 - Let S be a subset of an n-dimensional vector space...Ch. 4.5 - Let H be an n-dimensional subspace of an...Ch. 4.5 - Prob. 36ECh. 4.6 - Let B = {b1, b2} and C = {c1, c2} be bases for a...Ch. 4.6 - Let B = {b1, b2} and C = {c1, c2} be bases for a...Ch. 4.6 - Let u = {u1, u2} and w = {w1, w2} be bases for V,...Ch. 4.6 - Let A = {a1, a2, a3} and D = {d1, d2, d3} be bases...Ch. 4.6 - Let A = {a1, a2, a3} and B = {b1, b2, b3} be bases...Ch. 4.6 - Let D = {d1, d2, d3} and F = {f1, f2, f3} be bases...Ch. 4.6 - In Exercises 7-10, let B = {b1, b2} and C = {c1,...Ch. 4.6 - In Exercises 7-10, let B = {b1, b2} and C = {c1,...Ch. 4.6 - In Exercises 7-10, let B = {b1, b2} and C = {c1,...Ch. 4.6 - In Exercises 7-10, let B = {b1, b2} and C = {c1,...Ch. 4.6 - In 2 find the change-of-coordinates matrix from...Ch. 4.6 - In 2 find the change-of-coordinates matrix from...Ch. 4.6 - Exercises 15 and 16 provide a proof of Theorem 15....Ch. 4.6 - Prob. 18ECh. 4.6 - Prob. 19ECh. 4.6 - [M] Let P=[121350461],v1=[223],v2=[852],v3=[726]...Ch. 4.6 - Let B = {b1, b2}, C = {c1, c2}, and D = {d1, d2}...Ch. 4.8 - Verify that the signals in Exercises 1 and 2 are...Ch. 4.8 - Prob. 2ECh. 4.8 - Prob. 3ECh. 4.8 - Show that the signals in Exercises 3-6 form a...Ch. 4.8 - Show that the signals in Exercises 3-6 form a...Ch. 4.8 - Show that the signals in Exercises 3-6 form a...Ch. 4.8 - Prob. 7ECh. 4.8 - Prob. 8ECh. 4.8 - Prob. 9ECh. 4.8 - Prob. 10ECh. 4.8 - Prob. 11ECh. 4.8 - Prob. 12ECh. 4.8 - In Exercises 13-16, find a basis for the solution...Ch. 4.8 - In Exercises 13-16, find a basis for the solution...Ch. 4.8 - In Exercises 13-16, find a basis for the solution...Ch. 4.8 - In Exercises 13-16, find a basis for the solution...Ch. 4.8 - Exercises 17 and 18 concern a simple model of the...Ch. 4.8 - Exercises 17 and 18 concern a simple model of the...Ch. 4.8 - Prob. 21ECh. 4.8 - A lightweight cantilevered beam is supported at N...Ch. 4.8 - Prob. 25ECh. 4.8 - Prob. 26ECh. 4.8 - Prob. 27ECh. 4.8 - Prob. 28ECh. 4.8 - Prob. 29ECh. 4.8 - Prob. 30ECh. 4.8 - Prob. 31ECh. 4.8 - Write the difference equations in Exercises 29 and...Ch. 4.8 - Prob. 33ECh. 4.8 - Prob. 34ECh. 4.8 - Let yk = k2 and zk = 2k|k|. Are the signals {yk}...Ch. 4 - Find a basis for the set of all vectors of the...Ch. 4 - Let u1=[246], u2=[125], b=[b1b2b3], and W =...Ch. 4 - Explain what is wrong with the following...Ch. 4 - Consider the polynomials p1(t) = 1 +t, p2(t) = 1 ...Ch. 4 - Prob. 24SECh. 4 - Prob. 25SECh. 4 - Prob. 26SECh. 4 - Let T : n m be a linear transformation. a. What...Ch. 4 - Prob. 28SECh. 4 - Let S be a finite minimal spanning set of a vector...Ch. 4 - Prob. 30SECh. 4 - Prob. 33SECh. 4 - The concept of rank plays an important role in the...Ch. 4 - Determine if the matrix pairs in Exercises 19-22...Ch. 4 - Determine if the matrix pairs in Exercises 19-22...Ch. 4 - Determine if the matrix pairs in Exercises 19-22...Ch. 4 - Prob. 40SE
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- 3. A scientist recorded the movement of a pendulum for 10 s. The scientist began recording when the pendulum was at its resting position. The pendulum then moved right (positive displacement) and left (negative displacement) several times. The pendulum took 4 s to swing to the right and the left and then return to its resting position. The pendulum's furthest distance to either side was 6 in. Graph the function that represents the pendulum's displacement as a function of time. Answer: f(t) (a) Write an equation to represent the displacement of the pendulum as a function of time. (b) Graph the function. 10 9 8 7 6 5 4 3 2 1 0 t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -1 -5. -6 -7 -8 -9 -10-arrow_forwardA power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: h = −82.5 cos (3πt) + 97.5 where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes. (a) What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model. (b) Will the last passenger to board the ride need to wait in order to exit the ride? Explain.arrow_forwardThe Colossus Ferris wheel debuted at the 1984 New Orleans World's Fair. The ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The height above ground, h, of a passenger on the ride is a periodic function of time, t. The graph displays the height above ground of the last passenger to board over the course of the 15 min ride. Height of Passenger in Ferris Wheel 180 160 140- €120 Height, h (ft) 100 80 60 40 20 0 ך 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time of operation, t (min) Sine function model: h = −82.5 cos (3πt) + 97.5 where h is the height of the passenger above the ground measured in feet and t is the time of operation of the ride in minutes. What is the period of the sine function model? Interpret the period you found in the context of the operation of the Ferris wheel. Answer:arrow_forward
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