Linear Algebra Questions and Answers

The discrete system with transfer function H z O 1 BIBO stable if the system zero at 2 is canceled O 2 Unstable O 3 Asymptotically stable O 4 None of the answers O 5 BIBO stable Z 2 Z 0 8 2 z 0 8 is

You are considering purchasing a dump truck The truck will cost 74 000 and have operating and maintenance cos that start at 15 000 the first year and increases by 1 000 per year Assume that the salvage value at the end of fiv years is 17 000 and interest rate is 15 What is the equivalent annual cost of owning and operating the truck for five years Click the icon to view the interest factors for discrete compounding when i 15 per year The equivalent annual cost of owning and operating the truck is Round to the nearest dollar

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Consider the following lines of C int X Y int z 10 x z y x x 15 cout z is Z endl What is their result Print z is 10 to standard out Print z is 15 to standard out The code will not compile due to a type error None of these options describes the behavior of this code

Question 10 Given the following definition and initialization complete the statement below using the pointer raptor to call the public member function getDino for the object Assume the function s return type is string Dinosaur raptor new Dinosaur Raptor string name write the code to complete this statement here

25 to 69 beats per minute Let x be a random variable that represents the resting heart rate for an adult horse Assume that x has a distribution that is approximately normal USE SALT a The empirical rule indicates that for a symmetric and bell shaped distribution approximately 95 of the data lies within two standard deviations of the mean 95 20 20 Therefore a 95 range of data values extending from 20 to 20 is often used for commonly occurring data values Note that the interval from 20 to 20 is 40 in length This leads to a rule of thumb for estimating the standard deviation from a 95 range of data values Estimating the standard deviation For a symmetric bell shaped distribution standard deviation range high value low value where it is estimated that about 95 of the commonly occurring data values fall into this range Use this rule of thumb to estimate the standard deviation of x distribution in beats per minute beats per minute b What is the probability that the heart rate is less than 29 beats per minute Round your answer to four decimal places c What is the probability that the heart rate is greater than 61 beats per minute Round your answer to four decimal places d What is the probability that the heart rate is between 29 and 61 beats per minute Round your answer to four decimal places e A horse whose resting heart rate is in the upper 10 of the probability distribution of heart rates may have a secondary infection or illness that needs to be treated What is the heart rate corresponding to the upper 10 cutoff point of the probability distribution Round your answer to the nearest whole number minuta

1 2 Solve the equation 4 n 2n 6 1 The solution set is 3 0 0 6 0 0 1

EACH PROBLEM WILL BE GRADED 0 12 1 Check if the following formula is a tautology p r q p p q r p 1000 goticfy the following

17 18 and 3 19 The slope of the line is 20 00 21 22 Determine the slope of the line passing through the given points Write your answer in exact simplified form 5 2 4 3 23 24

Evaluate the function f x x 6x for the given value of x Simplify your answer f x h

olve the Inequality and write the solution set in Interval notation if possible Write numbers as simplified fractions or Integers 8 4x 19 5 The solution set is DO 0 0 Innl

A 3 1 Point J C H G uppose we want to remove F In a binary search tree we nev emove a node with two children Instead we replace it with nother node Which node will take the place of F K Q3 2 1 Point G Save Answer Q3 3 H After removing the node containing the original G is the result a red black tree Yes No int K Last saved on Jan 27 at 9 01 AM Now we want to remove C from the preceding tree That s a black leaf so we can t just remove it Instead we bubble up Afterwards what is the color of B red black Save Answer Last saved on Jan 27 at 9 04 AM

Consider the following scenario The rate of increase in the number of people who have committed drug crimes in a particular country who used crystal methamphetamine commonly called Ice in this country from 2006 to 2016 can be modeled by the rate function 355 70 1x 0 f x 6 x 16 otherwise where x represents the number of years since 2000 and f x represents the rate of increase in the number of people who have committed drug crimes who used Ice per year Compute the area under f x on the interval 11 x 15 Round your answer to the nearest whole number Interpret the result The area under f x on the interval 11 x 15 describes the total increase in the number of people who have committed drug crimes who used Ice from 2011 to 2015 The area under f x on the interval 11 x 15 describes the total increase in the rate of change in the number of people who have committed drug crimes who used Ice from 2011 to 2015 The area under f x on the interval 11 x 15 describes the number of people who have committed drug crimes who used Ice in 2011 The area under f x on the interval 11 x 15 describes the rate of change in the number of people who have committed 2011

Determine the area of the trapezoid in square units with the given dimensions b 2 4 h 8 2 h 4 8 square units

Determine the area in square units of the trapezoid shown in the figure Consider lengths to be standard unit 0 35 square units 4 1 0 6

Use this table to convert 13 494 millimeters to fraction inches in

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The scatter plot shows the time spent studying compared to test scores for Mr Stone s eighth grade class Predict th score that a student would earn if she studied for 7 hours Round your answer to the nearest whole number Enter your answer in the box Test Scores 90 80 70 60 50 0 Ay 0 2 4 6 8 10 Time Spent Studying h

Type your answers in all of the blanks and submit X X 2 A machine fills bags with 16 oz of sugar Then another machine weighs the bag If the weight of the bag differs by more than 0 3 oz the bag is considered defective Write and solve an absolute value equation to find the lightest and heaviest weights X for the accepted bags of sugar a The absolute value equation that represents this situation is your answer heaviest weight approved is TYPE YOUR Bswer her Write your response here b Solve the equation Based on the equation the lightest weight approved is Type your answer here 02 Do not enter any spaces in oz and the

PROBLEM 3 For a tuple of vectors A 3p p 3p 2p 3 1 p 3 2p 1 1 p 1 in R 3p verify if A is a basis of R 3p find a basis and the dimension of span A 4p verify if p 7 p 1 2p 5 e span A

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b log 6216 3 O 3 729 O 216 36 O 6 216 0 36 216

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Find the time constant t of the output current i t given the circuit in Fig P7 7 Given R1 6 kQ R2 14 kQ R3 11 KQ R4 11 k0 and C 206 F 6V R1 kn www Figure P7 7 R2 k i t C F Notes on entering solution R3 k ww t 0 Enter your solution in seconds Enter your solution to 2 decimal points Do not include units in your answer ex 5 seconds is entered as 5 00 R4kQ

4 Consider the following vectors in R V 141214 U 0 V3 Let V Span 7 U2 U3 a Determine if each of the following aree vectors is in V If so write it as a linear combination of 1 2 and 73 If not show work explaining why 15 0 8 and let W Span w Determine all vectors in R which are in both V and b Now let W hint without doing any work you can determine that there is at least one

The Northwest regional manager of an outdoor equipment retailer conducted a study to determine how managers at three store locations are using their time A summary of the results are shown in the following table Store Location 100 r 90 80 70 60 50 40 30 20 10 0 Bend 100 90 80 Portland 70 60 Seattle Percentage of Manager s Work Week Spent on Bend Meetings 18 52 32 Reports Portland 11 Seattle 11 17 Customers Idle a Create a stacked bar chart with store location on the horizontal axis and percentage of time spent on each task on the vertical axis 100 p 90 80 70 60 50 Idle Customers Reports Meetings 52 Idle Curtomers 24 37 4 19 100 90 80 70 60 50 40 30 20 10 0 13 14 Bend Portland Seattle Idle Customers Reports Meetings 40 30 20 10 0 Bend Portland Seattle Idle Cus Rep Mee

2 Suppose that a linear system has fewer equations than variables What can you determine about the solution set of the system

2 For an arbitrary set of numbers S define S S to be the set of all sums x y where and y are in S Let A B C D be sets of integers such that AUB AUB CUD CUD For example if AB C D 1 2 then AUB AUB CUD CUD 1 1 1 2 2 1 2 2 2 3 4 1

he following signal has To x t A To 2 To 1 Non symmetric real coefficients with non zero DC component 2 imaginary coefficients with non zero DC component 3 Complex coefficients with non zero DC component 4 Complex coefficients with zero DC component None of the answers

Use the figure below which shows the graph of y f x to answer the following questions 4 Click on the graph to get a larger version A Estimate the integral f f x dx 11 You will certainly want to use an enlarged version of the graph to obtain your estimate

Task 3 3p A stuntman attempted to jump across the street on his motorcycle speeding with initial velocity of 20 m s The takeoff ramp was inclined of 60 above horizontal The top of the truck on which he wanted to land was 5 m below the edge of the ramp The truck is moving towards the stuntman with 1 m s At what minimum distance D the truck should be located for the stuntman to land safely

Consider the function f x M 4 7x 3x 6X Determine the number of discontinuities of f x Determine the values of x at which f x has a discontinuity Enter your answer as a comma separated list of values The order of the values does not matter Enter DNE if f x does discontinuities

Limits Continuity Course Packet on limits Determine whether each statement is true or false You have one submission for each statement a For every function f x if lim f x does not exist then lim f x does not exist x13 x a True False b For every function f x if lim f x exists then lim f x exists x a x a True False c For every function f x if lim f x exists then lim f x also exists x at x a True False d For every function f x if lim f x and lim f x both exist then lim f x also exists x a x a True False e For every function f x if lim f x does not exist then lim f x does not exist x a x a True False x a f For every function f x if lim f x does not exist then lim f x does not exist x a True False

Does crime pay The FBI Standard Survey of Crimes showed that for about 80 of all property crimes burglary larceny car theft etc the criminals are never found and the case is never solvedt Suppose a neighborhood district in a large city suffers repeated property crimes not always perpetrated by the same criminals The police are investigating ten property crime cases in this district LUSE SALT a What is the probability that none of the crimes will ever be solved Round your answer to three decimal places 0 107 b What is the probability that at least one crime will be solved Round your answer to three decimal places 0 893 c What is the expected number of crimes that will be solved 2 crimes What is the standard deviation Round your answer to two decimal places x crimes d What is the smallest number of property crimes in that the police must investigate before they can be at least 90 sure of solving one or more cases crimor

Richard has just been given an 8 question multiple choice quiz in his history class Each question has five answers of which only one is correct Since Richard has not attended class recently he doesn t know any of the answers Assuming that Richard guesses on all eight questions find the indicated probabilities Round your answers to three decimal places USE SALT a What is the probability that he will answer all questions correctly 0 0000001 b What is the probability that he will answer all questions incorrectly 0 1677721 c What is the probability that he will answer at least one of the questions correctly Compute this probability two ways First use the rule for mutually exclusive events and the probabilities shown in the binomial probability distribution table 0 8322278 Then use the fact that P r 2 1 1 P r 0 0 8322278 Compare the two results Should they be equal Are they equal If not how do you account for the difference They should be equal but differ substantially They should be equal but may differ slightly due to rounding error They should not be equal but are equal They should be equal but may not be due to table error d What is the probability that Richard will answer at least half the questions correctly

If lim Ax 10x Bx 5 what is A B for positive A B X Select one O O O O b 4 d 8

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The owner of the Adelaide Australia Computer Hardware Company must decide among building 100 servers building 5000 hard drives or leasing all their equipment to another company The profit that will result from each alternative will be determined by whether material costs remain stable increase moderately or increase significantly In the payoff table below the estimated profits losses are given in thousands Material Costs sion Stable Servers Hard Drives Leasing mine the best decision using the Maximin decision criterion 1830 950 Moderate Increase 1030 2150 1100 550 Decision Leasing based on 2400 min 190 950 2400 Decision Hard Drives based on 950 max 190 950 2400 Decision Stable based on 950 max 950 550 2400 Decision Servers based on 190 min 190 950 550 Significant Increase 190 1150 2400

Simplify the expression by first getting a common denominator then pulling out any common factors in the numerator and finally expanding and or combining like terms from the remaining fact 2x 1 5 6 x 1 8 2x 1 x 1

Calculators were purchased at 50 per dozen and sold at 15 for three calculators What is the profit on six dozen calculators The profit is S

Let A and B be two events defined on the same sample space with p A 0 6 P B 0 3 and p AUB 0 7 then p AUB O a 0 6 O b 0 8 O c 0 7 d 0 4 0 2 O e

Find the inverse of the matrix if it exists If an answer does not exist enter DNE 2 1 1 3 5 10 16 19

Solve for X in the equation given A a 3X 2A B X b 2A 5B 3X X 11 c X 3A 2B 0 X d 11 6X4A 38 0 11 11 11 5 0 4 2 3 and B NHA 2 4 1 2 1

Perform the indicated operations when A A IA 0 1 1 2

Find the matrix product ABC by grouping the factors as AB C and grouping the factors as A BC Show that you obtain the same result from both processes C 0 1 1 1 1 6 0 A 4 B 4 9 33 a AB 8 AB C b BC 11 A BC 11

sider the following matrices 1 0 0 Z 1 a Find scalars a and b such that Z ax by a b X 1 Y 2 W a b c 1 1 b Do there exist scalars a and b such that W ax bY Yes O No c If ax bY CW 0 is it true that a b c 0 Yes O No d Find scalars a b and c not all equal to zero such that aX bY cZ C

0 2 1 A 213 8 1 and c B C Perform the indicated operations given A B C A

Express the column matrix b as a linear combination of the columns of A Use A A2 and A3 respectively for the columns of A 1 1 2 43 b 1 3 3 b A

nd if possible A B A B 24 2A B and B A If not possible enter IMPOSSIBLE in any single cell 38 0 A 3 6 1 30 1 a A B E 8 11 b A B c 24 E d 2A B E e B A B 8 11 11 K