Linear Algebra Questions and Answers

State why the system of equations must have at least one solution Select all that apply 3x 3y Z 0 6x 3y 3z 0 3x 9y 11z 0 During the elimination process we obtain the equation 0 0 O The point x y z 1 1 1 solves the system The system contains three equations and three variables The point x y z 0 0 0 solves the system During the elimination process we obtain a false statement Solve the system and determine whether it has exactly one solution or infinitely many solutions If the system has an infinite number of solutions xpress x y and z in terms of the parameter t x y z

Find a system of two equations in three variables X X2 and x3 that has the solution set given by the parametric representatio X t X s and x3 7 s t where s and t are any real numbers Enter your answer as a comma separated list of equations Show that the solutions to the system can also be written as X 7 s t x s and x3 t X1 t X2 S x3 x3 x3 x2 Let x S X3 t then x X1 s t X2X1

Activity Node A 1 B 1 C 2 D 3 Start Finish Node 2 3 4 4 Multiple Choice O What is the estimated expected mean time for activity D O 32 days 42 days 40 days Optimistic 41 54 58 32 41 days Duration days Most Likely 50 60 70 41 Pessimistic 59 66 82 44

Read the following sentence which contains gra We verified her medical degree none of us thought she was lying about that but not her claim to have given herself a heart transplant we re not that gullible Which revision best corrects the sentence Select one We verified her medical degree none of us thought she was lying about that but not her claim to have given herself a heart transplant we re not that gullible We verified her medical degree none of us thought she was lying about that but not her claim to have given herself a heart transplant we re not that gullible We verified her medical degree none of us thought she was lying about that but not her claim to have given herself a heart transplant we re not that gullible We verified her medical degree none of us thought she was lying about that but not her claim to have given herself a heart transplant we re not that gullible

Which of the following sentences uses punctuation correctly to help signal that missing information will follow Select one O This morning I had my very favorite breakfast french toast scrambled eggs and orange juice O This morning I had my very favorite breakfast french toast scrambled eggs and orange juice O This morning I had my very favorite breakfast french toast scrambled eggs and orange juice O This morning I had my very favorite breakfast french toast scrambled eggs and orange juice

A construction crew is lengthening a road Let be the total length of the road in miles Let D be the number of days the crew has worked Suppose that L 2D 300 gives L as a function of D The crew can work for at most 90 days dentify the correct description of the values in both the domain and range of the function Then for each choose the most appropriate set o values Domain Range Description of Values Onumber of days the crew has worked Olength of the road in miles Onumber of days the crew has worked Olength of the road in miles Set of Values Choose one Choose one

A small publishing company is planning to publish a new book Let C be the total cost of publishing the book in dollars Let N be the number of copies of the book produced For the first printing the company can produce up to 300 copies of the book Suppose that C 10N 600 gives C as a function of N during t first printing Identify the correct description of the values in both the domain and range of the function Then for each choose the most appropriate set of values Domain Range Description of Values Onumber of copies produced O cost of publishing book in dollars Onumber of copies produced O cost of publishing book in dollars Set of Values Choose one Choose one

A construction crew is lengthening a road Let L be the total length of the road in miles Let D be the number of days the crew has worked Suppose that L 3D 400 gives L as a function of D The crew can work for at most 80 days Identify the correct description of the values in both the domain and range of the function Then for each choose the most appropriate set of values Domain Range Description of Values Olength of the road in miles O number of days the crew has worked Olength of the road in miles Onumber of days the crew has worked Set of Values Choose one Choose one

The fuel tank of a certain airplane can hold up to 300 gallons of fuel Let W be the total weight of the airplane in pounds Let F be the total amount of fuel in its tank in gallons Suppose that W 7F 5000 gives W as a function of F dentify the correct description of the values in both the domain and range of the function Then for each choose the most appropriate set of values Domain Range Description of Values Oweight of airplane in pounds O amount of fuel in airplane s tank in gallons Oweight of airplane in pounds Oamount of fuel in airplane s tank in gallons Set of Values Choose one Choose one

21 What type of exponential function is this f x 0 85 3 5 Growth or decay How do you know What is the percent rate of change of the function

The time plot in the figure below gives the number of state and federal prisoners per 100 000 population t 450 400 350 300 Number per 100 000 250 200 150 100 50 OL 1980 1982 1984 1986 1988 1990 1992 1994 a Estimate the number of prisoners per 100 000 people for 1980 140 prisoners Estimate the number of prisoners per 100 000 people for 1997 444 prisoners 1996 b During the time period shown there was increased prosecution of drug offenses longer sentences for common crimes and reduced access to parole What does the time series graph say about the prison population change per 100 000 people The number of inmates per 100 000 increased every year c In 1997 suppose the U S population was approximately 266 575 000 people At the rate of 444 prisoners per 100 000 population about how many prisoners were in the system X prisoners Supporo the population was bo 227 500 000 in the year 2030 If the rate of oriconors por 100 000 stave

Evaluate each expression using the graphs of y f x and y g x shown below a f g 8 b g f 3 c f g 4 f g f g 2 d g f 7 e f f 3 a f g 8 Type a whole number C 10 9 8 7 YA 6 5 3 2 0 y f x A y g x 1 2 3 4 5 6 7 8 9

2 Determine the perimeter of the triangle 6 A 5 2 YA 61 A 2 20 ON C 1 7 24 2 6 B 4 1 Ax

Systems 1 Create three different scenarios that can be modeled using linear systems 2 Solve each scenario using a different method graphing substitution elimination 18 100y no 29sed note 23001 st Yosmaye to exs add suley ismitge sob

Consider the real number line shown here Determine whether the following number is between the two plotted values Yes 4 77 2 37 5 4 3 2 1 0 1 2 3 4 5 No 3 38

Alexis is making quarterly contributions of of 500 to her savings account which pays interest at the APR of 8 3 compounded quarterly Right after Alexis makes her 54th contribution the bank changes the APR to 9 and Alexis makes 36 more 500 contributions What is Alexis s balance right after her last contribution

Suppose you invest 150 a month for 8 years into an account earning 96 compounded monthly After 8 years you leave the money without making additional deposits in the account for another 23 years How much will you have in the end Suppose instead you didn t invest anything for the first 8 years then deposited 150 a month for 23 years into an account earning 996 compounded monthly How much will you have in the end Question Help Video Video 2

Suppose the quantity demanded g of a product when the price is p dollars is given by the equation p 553 5g and the quantity supplied is given by the equation p2g Find the equilibrium price and quantity Equilibrium quantity Equilibrium price items

Graph the solution set to the follow system of inequalities by drawing a polygon around the solution region Click to set the corner points 1 4y 24 5x 3y 35 10 9 DE 8 6 10 A 544 N M

Graph the feasible region for the follow system of inequalities by drawing a polygon around the feasible region Click to set the corner points y 3z 8 5y 3x2 24 y z 26 V z S8 20 20 NA X 2955 PAT535 2 ne My Clear All Draw Polygon 4 8920 2

c Use the duality principle to find out the dual of the following equation a b c d a c a d b c b d

Problem 5 Compute the following limits 1 lim 0 x sin 0 2 limx 0 3 T 9 3 limx 2 f x knowing that x 6x 12x 3 f x x 4x 9 x 3

uations have 4 as a solution 6 y 2 y 9 13 3y 12 24 y 7 Select all the equations that have 4 as a solution A 3y 12 OB 6 y 2 DC 24 y 7 OD y 9 13

10 Find E Y for the joint pdf given by f x y 0 y x 1 0 elsewhere Hint Use a double integral with order of integration dydx

Cumpany needed a new building It found a suitable location with an existing old building on the land The company reached a agreement to buy the land and the old building for 929 000 cash The old building was demolished to make way for the needec new building Following is information regarding the demolition of the old building and construction of the new one Construction cost of new building Cost for parking lot Demolition of old building Prepare a single journal entry to record the above costs assuming all transactions are paid in cash View transaction list View journal entry worksheet No A Transaction 1 Building Land Land improvements Cash 8 906 000 336 000 236 000 General Journal Debit 8 906 000 Credit

5 Three vectors a b and c are mutually perpendicular with b 1 and c 2 If the vectors p 2a 3b 4c and q a 2b 3c are perpendicular calculate the magnitude of the projection of the vector p on the vector a A 4 B 31 C 1 D 6

3 7 pts Find c if a 2 52 b 3 79 and C 41 6 Round to two decimal places if needed Assume A is the angle opposite side a B is the angle opposite side b and Cis the angle opposite side c You must draw the triangle to get credit for this problem

1 I zx x n

6 Data was collected on the speed and mileage of a car Speed is miles per hour and mileage is miles per gallon speed Y mileage 12 17 18 22 22 26 28 29 35 29 a Is the data Linear Quadratic or Cubic 40 31 b Write the equation of the regression curve 46 33 50 32 56 28 61 26 68 24 76 18 2 points AT 2 points c Use your equation to predict the mileage of a car with a speed of 42 miles per hour 2 points d What is the average rate of change from 55 miles per hour to 60 miles per hour 2 points

For the proprablility distribution table below P x 0 19 H 8 0 1 2 3 x 4 0 1 2 Find the mean Round to two decimal places 3 4 0 11 x 0 19 0 24 0 27 x Find the standard deviation Round to three decimal places xP x 00000 x P x 1000

Question 31 of 38 A group of young adults who were asked which issues would be important during the next decade gave the following answers 15 believed that nuclear war terrorism and environmental concerns would be important 40 believed that nuclear war would be important 18 believed that nuclear war and terrorism would be important 22 believed that nuclear war or terrorism but not the environment would be important 27 believed that nuclear war and the environment would be important 19 believed that terrorism but not nuclear war would be important 6 believed that only the environment would be a serious issue 8 believed that none of these issues would be important Complete parts a through c test 38 point s possible This question 1 point s possible Submit test a How many people were surveyed 155 people Simplify your answer b How many people believed the environment would be an important issue 90 people Simplify your answer c How many people believed only terrorism would be an important issue 52 people Simplify your answer

geographical locations If in North Dakota a 3 lb bag of apples sells for 6 and in in Minnesota it sells for 8 and the transportation costs are the same how would a seller react in North Dakota What change would occur in the North Dakota market Drag the supply curve on the graph below to show the new equilibrium point To refer to the graphing tutorial for this question type please click here 3 Price 2222 F 16 15 14 13 12 10 9 8 7 10 n 1 us that excluding trade barriers and transportation costs the price of a good tends to be the same in differen 55 Market for Apples in North Dakota LO O 9 7 D1 Quantity

Use the appropriate compound interest formula to compute the balance in the account after the stated period of time 14 000 is invested for 6 years with an APR of 3 and quarterly compounding The balance in the account after 6 years is Round to the nearest cent as needed

blem 1 Find the area of the parallelogram with vertices A 1 1 4 B 0 3 9 C 1 0 7 and D 2 2 12 0 Area

Be sure to fully justify your responses when appropriate Round probabilities to 4 decimal points Don t forge Units and use complete sentences when interpreting your result 8 pts A local hospital advertises that the average wait time in their emergency room is 16 minutes but we believe that it is longer than that After randomly collecting wait times from a sample of 35 patients we found that their average wait time was 16 7 minutes with a standard deviation of 5 92 minutes Run a test at the 05 significance level a What type of test are we using Determine if a test is left tailed right tailed or two tailed We are using a one sample test as this is appropriate for when we have a sample and want to compare the sample mean to a known population mean Since we re interested in whether the average wait time is significantly less than or greater than 16 minutes this is a two tailed test b o we meet the assumptions for normality for this type of test justify your response

10 pts In September 2007 only 48 of working class households said their incomes were falling behind the cost of living A survey of 50 random working class households in early February 2008 found that 32 of them now felt their incomes were falling behind Do these data provide sufficient evidence at the 0 01 level of significance to conclude that the proportion of working class households who say their incomes are falling behind the cost of living is higher in February 2008 than it was in September 2007 a What type of test are we using Determine if a test is left tailed right tailed or two tailed

Ex 2 Tia is contributing to the same project as Seth and has sampled a different group of students The proportion of freshmen in her sample is 0 40 or 40 Their proportion of freshmen are different Use the graph below created from the results of 50 samples to determine whose result is a better representation of the population Number of Samples Results of 50 Samples in 6 samples out of SQ between 30 and 35 participants are In 47 samples out of 50 the sample proportion fals between 1 and 0 35

Find the consumers surplus and the producers surplus at the equilibrium price level for the given price demand and price supply equations Include a graph that identifies the consumers surplus and the producers surplus Round all values to the nearest intege p D x 70 0 06x p S x 20 0 001x I What is the consumers surplus CS CS Round to the nearest integer as needed Round all intermediate steps to the nearest integer

Violent crimes include rape robbery assault and homicide The following is a summary of the violent crime rate violent crimes per 100 000 population for all states of a country in a certain year Complete parts a through d Q 271 8 Q 388 5 Q 529 7 a Provide an interpretation of these results Choose the correct answer below OA 25 of the states have a violent crime rate that is 271 8 crimes per 100 000 population or more 50 of the states have a violent crime rate that is 388 5 crimes per 100 000 population or more 75 of the states have a violent crime rate that is 529 7 crimes per 100 000 population or more O B 25 of the states have a violent crime rate that is 271 8 crimes per 100 000 population or less 50 of the states have a violent crime rate that is 388 5 crimes per 100 000 population or less 75 of the states have a violent crime rate that is 529 7 crimes per 100 000 population or less OC 75 of the states have a violent crime rate that is 271 8 crimes per 100 000 population or less 50 of the states have a violent crime rate that is 388 5 crimes per 100 000 population or less 25 of the states have a violent crime rate that is 529 7 crimes per 100 000 population or less b Determine and interpret the interquartile range The interquartile range is crimes per 100 000 population Type an integer or a decimal Interpret the interquartile range Choose the correct answer below OA The middle 50 of all observations have a range of 116 7 crimes per 100 000 population OB All observations have a range of 257 9 crimes per 100 000 population OC The middle 25 of all observations have a range of 257 9 crimes per 100 000 population OD The middle 50 of all observations have a range of 257 9 crimes per 100 000 population c The violent crime rate in a certain state of the country in that year was 1 679 Would this be an outlier The lower fence is crimes per 100 000 population The upper fence is crimes per 100 000 population Round to two decimal places as needed The violent crime rate in n nortain state of the counter in that varume 1 670 Would this he an outlin

K The following table shows the number of cell phone subscriptions in a country in billions for selected years x after 2005 2006 1 4 X y 2005 0 5 O C 2007 4 1 2008 7 6 2009 9 1 a Find a function C x that models the data where x is years after 2005 b Predict the number of cell phone subscriptions in 2012 a Select the correct choice below and fill in the answer boxes within your choice Round to two decimal places as needed OA The best model for the data is an exponential function and is given by f x B The best model for the data is a logarithmic function and is given by f x Inx 2010 10 0 The best model for the data is a logistic function and is given by f x Point

Solve 9 x 2 83 XX Simplify your answer Type an integer or decimal rounded to four decimal places as needed

Verify the identity sin x sin x cot x csc x Choose the sequence of steps below that verifies the identity O A O B O C O D D sin x sin x cot x sinx 1 cot x sin x sinxcot x sinx 1 cot x sin x sin x cot2x 1 cot x csc x 1 csc x 1 CSC X 1 sinx sinx cot x sinx cot x 1 CSC X CSC X CSC X csc x csc x csc x csc x

Match each set of equations with the move that turned the first equation into the second 6z 9 42 3 2z 9 3 4 5r 7 18 52 7 4 5 8 10 752 4 10x 3 5x 5 4 4 52 16 12z 4 20z 24 3z 1 5z 6 DRAG DROP THE ANSWER cm 88

sing DeMoivre s theorem find 3 j 5 3 j 5 cos j sin Simplify your answers Round to two decimal places as needed Type any angle measures in degrees Use angle measures greater than or equal

Prove the given identity csc 0 sin 0 cos 0 cot 0 Choose the correct proof below OA csc 0 sin 0 OB csc 0 sin 0 OC csc 0 sin 0 OD csc 0 sin 0 1 sin e 1 sin 0 1 sin 0 sin 0 1 sin e sin 0 sec 0 sin 0 sin 0 1 sin 0 1 sin 20 sin 0 1 sin 0 2 sin 0 sin 0 1 sin 0 2 sin 0 2 cos 0 sin 0 sin e cos 0 2 sin e s20 cos 2 Question cos 0 cot 0 cos 20 sin 0 cos 0 cot 0 cos 0 cot 0 cos 0 cot 0

Verify the identity cos 0 tan 0 sin 0 Which of the following four statements verifies the identity OA cos 0 tan 0 1 sin 0 OB cos 0 tan 0 cos 0 OC cos 0 tan 0 cos e sin 0 OD cos 0 tan 0 sin 0 cos 0 sin 0 cos e cos e sin e cos 0 sin e cos sin 0 sin 0 cos sin 0 cose cos sin e sin 0 cos 0 sin 0 cos e sin 0 sin 0 sin 0 sin 0

Verify the identity csct 1 cott OB Choose the sequence of steps below that verifies the identity O A O C O D csct 1 csct 1 csct 1 cott cott csct 1 csct 1 cott cott csct 1 csct 1 cott csct 1 cott csct 1 cott csct 1 csct 1 cott csct 1 csct 1 csct 1 csc t 1 csct 1 cott csct 1 csct 1 cott csct 1 csc t 1 cott csct 1 csc t 1 cott csct 1 Question 10 of 10 cot t cott csct 1 cot t cott csct 1 cot t cott csct 1 csc t 1 cot t cott csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1

Assign 1 point If x 2 0 4 and 7 5 find tan 0 where is the angle between 7 and w tan 0

3 Use Householder s method to transform the following matrix into tridiagonal form 1 A 1 2 1 2

5 Evaluate the following function at the given value of the variable f x 3x 4x 6 7 pts f 3 f 0 6 Graph the linear function y 6 8x on the given graph paper State the slope and y intercept of this line 7 pts It costs 7 A company that manufactures small canoes has a fixed cost of 24 000 40 to produce each canoe The selling price is 160 per canoe In solving this exercise let x represent the number of canoes produced and sold Determine the break even point 7 pts 8 At the time of her grandson s birth a grandmother deposits 3000 in an account that pays 2 compounded monthly What will be the value of the account at the child s twenty first birthday assuming that no other deposits or withdrawals are made during this period 7pts Use A P 1 nt 7 pts