Linear Algebra with Applications (2-Download)
5th Edition
ISBN: 9780321796974
Author: Otto Bretscher
Publisher: PEARSON
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Chapter 4.1, Problem 45E
To determine
To find a basis of the space
And thus determine the dimension of
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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
Linear Algebra with Applications (2-Download)
Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...
Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...Ch. 4.1 - Let V be the space of all infinite sequences of...Ch. 4.1 - Let V be the space of all infinite sequences of...Ch. 4.1 - Let V be the space of all infinite sequences of...Ch. 4.1 - Let V be the space of all infinite sequences of...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Prob. 31ECh. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Prob. 33ECh. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - If c is any vector in n , what are the possible...Ch. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - In the linear space of infinite sequences,...Ch. 4.1 - A function f(t) from to is called even if...Ch. 4.1 - Prob. 48ECh. 4.1 - Let L(m,n) be the set of all linear...Ch. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Make up a second-order linear DE whose solution...Ch. 4.1 - Show that in an n-dimensional linear space we can...Ch. 4.1 - Show that if W is a subspace of an n-dimensional...Ch. 4.1 - Show that the space F(,) of all functions from to...Ch. 4.1 - Show that the space of infinite sequences of real...Ch. 4.1 - We say that a linear space V is finitely generated...Ch. 4.1 - In this exercise we will show that the functions...Ch. 4.1 - Show that if 0 is the neutral element of a linear...Ch. 4.1 - Consider the sequence (f0,f1,f2) recursively...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 15ECh. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 21ECh. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 35ECh. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 41ECh. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 46ECh. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 48ECh. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Find the image, rank, kernel, and nullity of the...Ch. 4.2 - Find the image, rank, kernel, and nullity of the...Ch. 4.2 - Find the image and kernel of the transformation T...Ch. 4.2 - Find the image, rank, kernel, and nullity of the...Ch. 4.2 - Find the kernel and nullity of the transformation...Ch. 4.2 - Find the image and kernel of the transformation T...Ch. 4.2 - For the transformation T in Exercise 23, find the...Ch. 4.2 - For the transformation T in Exercise 42, find the...Ch. 4.2 - Find the image and kernel of the transformation T...Ch. 4.2 - Find the image and kernel of the transformation T...Ch. 4.2 - Define an isomorphism from P3 to 3 , if you can.Ch. 4.2 - Define an isomorphism from P3 to 22 , if you can.Ch. 4.2 - We will define a transformation T from nm to...Ch. 4.2 - Find the kernel and nullity of the linear...Ch. 4.2 - For which constants k is the linear transformation...Ch. 4.2 - For which constants k is the linear transformation...Ch. 4.2 - If matrix A is similar to B, is T(M)=AMMB an...Ch. 4.2 - For which real numbers co, c0,c1,...,cn is the...Ch. 4.2 - Prob. 71ECh. 4.2 - Prob. 72ECh. 4.2 - Prob. 73ECh. 4.2 - In Exercises 72 through 74, let Znbe the set of...Ch. 4.2 - Prob. 75ECh. 4.2 - Prob. 76ECh. 4.2 - Prob. 77ECh. 4.2 - Let + be the set of positive real numbers. On + we...Ch. 4.2 - Prob. 79ECh. 4.2 - Prob. 80ECh. 4.2 - Prob. 81ECh. 4.2 - Prob. 82ECh. 4.2 - Consider linear transformations T from V to W and...Ch. 4.2 - Prob. 84ECh. 4.3 - GOAL Use the concept of coordinates. Find the...Ch. 4.3 - GOAL Use the concept of coordinates. Find the...Ch. 4.3 - Do the polynomials...Ch. 4.3 - Consider the polynomials f(t)=t+1 and...Ch. 4.3 - Prob. 5ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 21ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 32ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - a. Find the change of basis matrix S from the...Ch. 4.3 - Prob. 45ECh. 4.3 - a. Find the change of basis matrix S from the...Ch. 4.3 - a. Find the change of basis matrix S from the...Ch. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - In Exercises 48 through 53, let V be the space...Ch. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - In Exercises 54 through 58, let V be the plane...Ch. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Consider a linear transformation T from V to V...Ch. 4.3 - In the plane V defined by the equation 2x1+x22x3=0...Ch. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 63ECh. 4.3 - Let V be the space of all upper triangular 22...Ch. 4.3 - Let V be the subspace of 22 spanned by the...Ch. 4.3 - Prob. 66ECh. 4.3 - Let V be the linear space of all functions of the...Ch. 4.3 - Consider the linear space V of all infinite...Ch. 4.3 - Consider a basis f1,...,fn , of Pn1.Let a1,...,an...Ch. 4.3 - Prob. 70ECh. 4.3 - Prob. 71ECh. 4.3 - In all parts of this problem, let V be the set of...Ch. 4.3 - Prob. 73ECh. 4 - The polynomials of degree less than 7 form a seven...Ch. 4 - Prob. 2ECh. 4 - Prob. 3ECh. 4 - Prob. 4ECh. 4 - The space 23 is five-dimensional.Ch. 4 - Prob. 6ECh. 4 - Prob. 7ECh. 4 - Prob. 8ECh. 4 - If W1 and W2 are subspaces of a linear space V,...Ch. 4 - If T is a linear transformation from P6 to 22 ,...Ch. 4 - Prob. 11ECh. 4 - Prob. 12ECh. 4 - Prob. 13ECh. 4 - All linear transformations from P3 to 22 are...Ch. 4 - If T is a linear transformation from V to V, then...Ch. 4 - Prob. 16ECh. 4 - Every polynomial of degree 3 can be expressed as a...Ch. 4 - a linear space V can be spanned by 10 elements,...Ch. 4 - Prob. 19ECh. 4 - There exists a 22 matrix A such that the space V...Ch. 4 - Prob. 21ECh. 4 - Prob. 22ECh. 4 - Prob. 23ECh. 4 - Prob. 24ECh. 4 - Prob. 25ECh. 4 - Prob. 26ECh. 4 - Prob. 27ECh. 4 - Prob. 28ECh. 4 - Prob. 29ECh. 4 - Prob. 30ECh. 4 - If W is a subspace of V, and if W is finite...Ch. 4 - Prob. 32ECh. 4 - Prob. 33ECh. 4 - Prob. 34ECh. 4 - Prob. 35ECh. 4 - Prob. 36ECh. 4 - Prob. 37ECh. 4 - Prob. 38ECh. 4 - Prob. 39ECh. 4 - Prob. 40ECh. 4 - Prob. 41ECh. 4 - The transformation D(f)=f from C to C is an...Ch. 4 - If T is a linear transformation from P4 to W with...Ch. 4 - The kernel of the linear transformation...Ch. 4 - If T is a linear transformation from V to V, then...Ch. 4 - If T is a linear transformation from P6 to P6 that...Ch. 4 - There exist invertible 22 matrices P and Q such...Ch. 4 - There exists a linear transformation from P6 to ...Ch. 4 - If f1,f2,f3 is a basis of a linear space V, and if...Ch. 4 - There exists a two-dimensional subspace of 22...Ch. 4 - The space P11 is isomorphic to 34 .Ch. 4 - If T is a linear transformation from V to W, and...Ch. 4 - If T is a linear transformation from V to 22 with...Ch. 4 - The function T(f(t))=ddt23t+4f(x)dx from P5 to P5...Ch. 4 - Any four-dimensional linear space has infinitely...Ch. 4 - If the matrix of a linear transformation T (with...Ch. 4 - If the image of a linear transformation T is...Ch. 4 - There exists a 22 matrix A such that the space of...Ch. 4 - If A, B, C, and D are noninvertible 22 matrices,...Ch. 4 - There exist two distinct three-dimensional...Ch. 4 - the elements f1,...,fn , (where f10 ) are linearly...Ch. 4 - There exists a 33 matrix P such that the linear...Ch. 4 - If f1,f2,f3,f4,f5 are elements of a linear space...Ch. 4 - There exists a linear transformation T from P6 to...Ch. 4 - If T is a linear transformation from V to W, and...Ch. 4 - If the matrix of a linear transformation T (with...Ch. 4 - Every three-dimensional subspace of 22 contains at...
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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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