Matrices & Determinants Questions and Answers

Given f 1 x 2 1 for 1 2 R apply inverse SR 1 update rule to f 1 22 with 8 H 1 69 Xk 0 1 3 1 3 2 3 2 3 1 F None of them T 1 a 2 to obtain the next iteration H 1 a b d Find the value of c

9 1 12 1 15 18 H 21 24 Question 20 2 5 points Salaries Jonah was paid 2900 to complete a landscaping job He had to purchase 1200 worth of materials to use for the project Then he worked a total of 98 hours on the project over 2 weeks by himself How much did he make per hour on the job 41 84 per hour 29 59 per hour

Question 21 2 5 points Salaries Sue Brown is a salesperson at a car dealer ship She earned a gross pay of 8000 for the month of June Her state tax rate is 3 5 of her taxable wages Assuming the full amount is taxable how much will Sue Brown owe in state taxes for the month 332 50 280 00

c 130 YYA Y YYY YYYY APPY A YYY d 602 T d of pp YY D YY

a Consider the following Write the percent represented by the shaded portion of the grid Find that percent of the given number 82 600 b Consider the following Write the percent represented by the shaded portion of the grid her

Mr Winking needs his computer hooked up to every station in the school Not every station is connected to every other station The cost of connecting various stations is represented in the graph below Mr Winking A 8 58 60 10 6 9 9 6 9 A 1 3 7 G E SF What is the cost of the minimum spanning tree using Kurskal s Algorithm 5 7 D H L 4

times and tasks that must be completed to create a school s yearbook Which EST graph below correctly represents the information in the table Scurt 0 Start 0 0 5 Start B 0 0 B 0 0 5 0 0 5 03 B 0 3 C 0 3 0 3 0 5 0 5 25 03 D 3 0 2 8 1 0 2 5 D 1 0 2 8 Start A Create a guest list B Create a list of snack foods party favors and decorations C Purchase Make Invitations snacks decorations party favors D Mail invitations at the post office E Wast for response to the RSVP on the invitation F Clean the apartment G Decorate for the party H Cook and set out spacks I Get Dressed and Ready J Host the Party K Clean Up Finish 36 E 4 0 36 36 E 3 8 36 39 8 D 3 8 E 1 0 36 39 8 F 3 5 G 43 5 40 1 2 H 1 5 40 F 3 5 G 39 8 43 3 3 5 44 7 H 15 I 39 8 413 H 41 3 I 1 0 1 2 F433 G 15 1 2 1 2 I 1 0 3 5 K 492 25 J 45 7 K 45 8 3 5 1 0 J 42 3 45 8 2 5 1 0 36 0 3 5 1 2 1 5 1 0 3 5 2 5 J 35 hours 10 0 5 03 FINISH 51 7 25 K 2 5 48 3 FINISH 49 3 FINISH 48 3 None None A B C D E F E G H I J

Question 5 8 34 points What is the correct adjacency matrix for the graph shown D O ABLD 10 B 0 10 CO 2 DI F A RUR44 1 E O 0 0 1 D SE CO 001 ROON CONO 00 0 0 10 10 2 1 10 1 10 1 0 1 1 1 2 1 20 1 1 1 FO 10 FI 0 UON 00 110 EF 1 10 1 0 0 1 0 0 0 1 10 1 10 0 1 1 0 1 0 10 0 0 0 1 1 0 0 F 1 0 10 F E A D B C

8 Completely Side EG 30 Angle DGF Angle GFD Angle FDG Side GF Side DF Angle EDG E 120 35 G 20

Determine the values of A for which the following system of equations has nontrivial solutions Enter your answers as a comma separated list 2 4 x 25 x 0 4x 2 7 x 0 A 8 1 Find the solutions for each value of J Use the parameter r to express the solutions smaller 2 x x I larger 2 X X

Find all solutions of the equation cosx sqrt 3 2

Compute d u v relative to the Euclidean norm the sum norm and the max norm 3 H de u v d u v 2 and v 100

A person is selected at random from a pool of twenty nine people consisting of fifteen men and fourteen women for a psychology study Find the probability that the person selected is the following Enter your probabilities as fractions

c In x 1 In x 3 In x 3 9 The exponential model describes the population A of a country in millions t years after 2003 Use the model to determine the population of the country in 2003 A 456 100 0141 The population of the country in 2003 was

Let A 24 13 and B a Find AB if possible b Find BA if possible 2 1 38 c Are the answers in parts a and b the same d In general for matrices A and B such that AB and BA both exist does AB always equal BA a Find AB if possible Select the correct choice below and if necessary fill in the answer box to complete your choice OA AB OB The product AB cannot be found b Find BA if possible Select the correct choice below and if necessary fill in the answer box to complete your choice No Yes A BA OB The product BA cannot be found c Are the answers in parts a and b the same no beth ovint 10 AD shunun anal DA

Question 3 20 points Euler Circuits Paths Which of the below descriptions shows a possible Euler Path ABCED ABCDE ABEDBCEA ABCAECDBED D B E

Time Taken Question 1 25 points Using the following EST graph to answer the question assuming the time unit is days 30 days 55 days 20 days START 175 days 0 0 0 14 14 E 25 How long does it take to do just Task G 10 30 30 D 24 10 G 55 F 55 20 35 120 30 H 90 5 125 50 FINISH 175

D 23 D x 29 and D y 13 What is the solution set of the system

Highlight A transit company operates commuter trains to help people get to the city each day Each train travels on a straight route to and from the farthest station stopping at other stations along the route The graph shows the distance y miles the train is from the station after x minutes Commuter Train Distance Distance from the Station miles S48525 30 0 10 20 30 40 50 60 70 80 Time minutes Formula Sheet Calculator Referen What is the farthest distance in miles that the train is located from the station at any time OA 100 OB 80 OC 40 D 20

1 Solve by GRAPHING Be sure to write solution y 3x 4 y x 2 Solution X 3 1 5 What your grows 4 3 N 2 1 50 3 NOIN 3 50 4 2 1 y 1 72 4 177 N tr 1 2 3 4

Below is the graph of f x x 2x 3x 4x 4 AY 1 Identify the following Domain Range 0 2 6 db 8 2 X x intercept s y intercept s Describe the end behavior of the graph by completing the following statements As x f x As xx

Show that A P 1 1 10 2 16 8 188 1 1 5 and B 11 12 18 6 9 8 6 are similar matrices by finding an invertible matrix P satisfying A PE

Solve correct to 2 decimal places 5 9 196 C

graph y 1 2x 1

e inner product u v 2 in 22 and the Gam Schmidt orthonormalization process to transform 2 1 2 6 into an orthonormal basis Use the vectors in the order in which they are given

K Use a system of linear equations to solve the following problem A new restaurant is to contain two seat tables and four seat tables Fire codes limit the restaurant s maximum occupancy to 72 customers If the owners have hired enough servers to handle 21 tables of customers how many of each kind of table should they purchase Write a system of linear equations using the given information Choose correct answer below OA OB O C OD 2x 4y 72 x y 21 x y 72 2x 4y 21 2x 4y 72 x y 21 x y 72 2x 4y 21 They should purchase two seat tables and four seat tables

K The function f x 7x 6 is one to one a Find an equation for f1 the inverse function b Verify that your equation is correct by showing that f f x x and f f x x a Select the correct choice below and fill in the answer box es to complete your choice Simplify your answer Use integers or fractions for any numbers in the expression OA F x for x OB f x for x Oc f x OD f x for all x The equation is for x b Verify that the equation is correct f r x f and f f x f 0 Substitute Simplify

The system of linear equations O has 0 solutions has exactly 2 solutions O has exactly 1 solution O has infinitely many solutions x 7y 2z Y z 2 2 2 0

Step 1 of 3 Use the following information to find f g x Answer 2 Points f g x 2x 4 3 f x 3x 4 2 and g x

Plot the point given in polar coordinates

Find the solution s of the equation in the interval 0 2 Use a graphing utility to verify your results Enter your answers as a comma separated 3 3 cos x 7 3 cos x 7 3 X X

The purpose of this question is to do the preliminary work to make a well labeled sketch of the graph of the function First find the critical values there should be three X Two of the critical values should be associated with asymptotes of this function The remaining critical value should be a local maximum What is the local maximum for this graph y f x 3x 9x 9 x 3x 28 Hint What is lim f x x In addition to the vertical asymptotes there is another asymptote Give the equation for this asymptote Finally give the range for the function f range

A car rental service in a certain town has a fleet of about 600 cars at three locations A car rented at one ocation may be returned to any of the three locations The various fractions of cars returned to the three ocations are shown in the matrix to the right Suppose that on Monday there are 195 cars at the airport or rented from there 65 cars at the east side office and 340 cars at the west side office What will be the approximate distribution of cars on Wednesday On Wednesday cars will be at the airport Round to the nearest integer as needed cars will be at the East location and Cars Rented From Airport East West 0 93 0 03 0 10 0 00 0 94 0 05 0 07 0 03 0 85 cars will be at the West location Returned To Airport East West

Let A 41 A 5 2 3 4 Compute 412 A and 41 A

REASONING A company s survey of 225 employees finds that employees consume on average 9 8 caffeinated drinks during the workweek with a margin of error of 0 3 a Give an interval that is likely to contain the exact number of drinks consumed in a workweek per person Between and b The company has 450 employees Estimate the number of caffeinated drinks consumed by all employees during the workweek Between and

Find the interval s where the function is increasing and the interval s where it is decreasing Enter your answers using interval notation 1 f x increasing DNE X decreasing 0 6 U 6 00 That s right

Write this number as a whole number or a decimal 5 69 x 10 2

10 2 1 11 Let A 2 1 3 and 3B x 2 1 If B is the inverse of the matrix A 3 1 1 1 1 y then what is x y A 2 B 4 C 6 D 8 E 10

In Exercises 23 26 express the matrix and its inverse as prod ucts of elementary matrices 24 12527 23 25 0 0 040 3 1 26 1 0 1 1 1

Fit a trigonometric function of the form f t co c sin t c cos t to the data points 0 1 5 2 9 3 2 using least square 0 1 5 13 535 25 035

Evaluate without a calculator If this is not a real number then write DNE 64 4 3

Find a the orthogonal projection of b onto Col A and b a least squares solution of Ax b A 14 18 14 b 9 4 5 a The orthogonal projection of b onto Col A is b Simplify your answers

Solve the system of equations using matrices Use the Gaussian elimination method with back substitution Use the Gaussian elimination method to obtain the matrix in row echelon form Choose the correct answer below O A x y z 5 5x y z 13 x 5y 4z 1 O C 100 5 0 2 1 1 1 1 1 1 1 0 1 8 7 1 5 1 2 00 1 8 B OD 11 5 1 01 2 00 1 8 1 1 1 5 0 1 1 2 00 1 8

Perform the row operation on the given augmented matrix 17 4 1 62 9 1 33 4 8 6R R What is the resultant matrix

45 Find the augmented matrix for the system 5x 7y z 7 5x 8z 5 8x y 7z 3 The augmented matrix for the system is 7 5 3

Determine the solution of the system of equations represented by the lines in the graph Check your solution by substituting into both equations 3x 4y 8 x 3y 11 10 Correct 1012 Enable Zoom Pan

19 Which of the following statements is true about the function below O A The y intercept of the function is at y 8 O B The maximum value of the function is 1 O C The x intercepts of the function are at x 4 and x 2 O D The minimum value of the function is 3 x 6x 8

Determine whether the given vector functions are linearly dependent or linearly independent on the interval 0 00 7t 6 4 7

Use a system of linear equations in three variables to solve the following problem A certain brand of razor blade comes in packages of 6 12 and 24 blades costing 2 3 and 4 per package respectively A store sold 17 packages containing a total of 216 razor blades and too in 48 How many packages of each type were sold Write a system of linear equations using the given information Choose correct answer below OA O C 6x 12y 24z 48 2x 3y 4z 216 x y z 17 2 6x 12y 24z 17 2x 3y 4z 216 x y z 48 There were packages of 6 blades packages of 12 blades and COCOS B D packages of 24 blades sold 6x 12y 24z 216 2x 3y 4z 48 x y z 17 6x 12y 24z 48 2x 3y 4z 17 x y z 216

Graph the line by locating any two ordered pairs that satisfy the equation Round to the nearest thousandth if necessary 3 y x 7 Answer Enter the coordinates to plot points on the graph Any lines or curves will be drawn once all required points are plotted A 107 SI Enable Zoom Pan 8