College Algebra with Modeling & Visualization (6th Edition)
6th Edition
ISBN: 9780134441795
Author: Rockswold
Publisher: PEARSON
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Chapter R3, Problem 54E
To determine
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Determine whether it's true or false and the reasoning is needed
1. (20 pts) Determine whether the following statements are true (T) or false (F)? (A
reasoning is required.)
(1) Let V be the set of all ordered pairs of real numbers. Consider the following
addition and scalar multiplication operations on u =
u= (u1, u2) and v =
(v1, v2): u + v = (U₁ + V₁, U₂ + v₂), ku = (ku₁, u₂). Is V a vector space
under the above operations?
U2
(2) The set Mmxn of all m×n matrices with the usual operations of addition
and scalar multiplication is a vector space.
α
(3) The dimension of the vector space of all matrices A = [a b] in R2×2 with
a+d=0 is 4.
(4) The coordinate vector of p(x) = 2-x+x² in P3 relative to the basis S =
{1, 1+x, x + x2} is [4 -2 1].
(5) If a 6×4 matrix A has a rank 3, then the dimension of N(A) is 3.
5. (20%) The linear transformation L: P3 → P2 defined by L(f(x)) = f'(x)+
f(0).
(a) Find the representing matrix A of L with respect to the ordered basis
{x2, x, 1} for P3, and the ordered basis {2,1 - x} for P2.
(b) Find the coordinates of the f(x) = 2x² +2 in P3 with respect to the
ordered basis {x2,-x, 1}, and find the coordinates of L(f(x)) with respect
to the ordered basis {2,1-x}
Chapter R3 Solutions
College Algebra with Modeling & Visualization (6th Edition)
Ch. R3 - Prob. 1ECh. R3 - Prob. 2ECh. R3 - Prob. 3ECh. R3 - Prob. 4ECh. R3 - Prob. 5ECh. R3 - Prob. 6ECh. R3 - Prob. 7ECh. R3 - Prob. 8ECh. R3 - Prob. 9ECh. R3 - Prob. 10E
Ch. R3 - Prob. 11ECh. R3 - Combine like terms whenever possible. 12....Ch. R3 - Prob. 13ECh. R3 - Prob. 14ECh. R3 - Prob. 15ECh. R3 - Prob. 16ECh. R3 - Prob. 17ECh. R3 - Prob. 18ECh. R3 - Prob. 19ECh. R3 - Prob. 20ECh. R3 - Prob. 21ECh. R3 - Prob. 22ECh. R3 - Prob. 23ECh. R3 - Prob. 24ECh. R3 - Prob. 25ECh. R3 - Prob. 26ECh. R3 - Prob. 27ECh. R3 - Prob. 28ECh. R3 - Prob. 29ECh. R3 - Prob. 30ECh. R3 - Prob. 31ECh. R3 - Prob. 32ECh. R3 - Prob. 33ECh. R3 - Prob. 34ECh. R3 - Prob. 35ECh. R3 - Prob. 36ECh. R3 - Prob. 37ECh. R3 - Prob. 38ECh. R3 - Prob. 39ECh. R3 - Prob. 40ECh. R3 - Prob. 41ECh. R3 - Prob. 42ECh. R3 - Prob. 43ECh. R3 - Prob. 44ECh. R3 - Prob. 45ECh. R3 - Prob. 46ECh. R3 - Prob. 47ECh. R3 - Prob. 48ECh. R3 - Prob. 49ECh. R3 - Prob. 50ECh. R3 - Prob. 51ECh. R3 - Prob. 52ECh. R3 - Prob. 53ECh. R3 - Prob. 54ECh. R3 - Prob. 55ECh. R3 - Prob. 56ECh. R3 - Prob. 57ECh. R3 - Prob. 58ECh. R3 - Prob. 59ECh. R3 - Prob. 60ECh. R3 - Prob. 61ECh. R3 - Prob. 62ECh. R3 - Prob. 63ECh. R3 - Prob. 64ECh. R3 - Prob. 65ECh. R3 - Prob. 66ECh. R3 - Prob. 67ECh. R3 - Prob. 68ECh. R3 - Prob. 69ECh. R3 - Prob. 70ECh. R3 - Prob. 71ECh. R3 - Prob. 72ECh. R3 - Prob. 73ECh. R3 - Prob. 74ECh. R3 - Prob. 75ECh. R3 - Prob. 76ECh. R3 - Prob. 77ECh. R3 - Prob. 78ECh. R3 - Prob. 79ECh. R3 - Prob. 80ECh. R3 - Prob. 81ECh. R3 - Prob. 82ECh. R3 - Prob. 83ECh. R3 - Prob. 84ECh. R3 - Prob. 85ECh. R3 - Prob. 86ECh. R3 - Prob. 87ECh. R3 - Prob. 88ECh. R3 - Prob. 89ECh. R3 - Prob. 90ECh. R3 - Prob. 91ECh. R3 - Prob. 92ECh. R3 - Prob. 93ECh. R3 - Prob. 94ECh. R3 - Prob. 95ECh. R3 - Prob. 96E
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- 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.arrow_forward2. 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?arrow_forward3. 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_forward
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