Linear Algebra Questions and Answers

5 Solve the following polynomial equation App a x54x x 4 0

3 Factor the following K a 4x 4x 16x 16 b x 64

2 Divide and state the answer in quotient form App g x f x x 4x 2x 3 g x x 2

The sitting height of a person is the vertical distance between the sitting surface and the top of the head The accompanying table lists sitting heights mm of randomly selected U S Army personnel collected as part of a large reputable study Using the data with a 0 05 significance level what do you conclude Click the icon to view the sitting height data OA Ho Sitting heights are not affected by handedness H Sitting heights are affected by handedness OB Ho Sitting heights are not affected by an interaction between gender and handedness H Sitting heights are affected by an interaction between gender and handedness OC Ho Sitting heights are not affected by gender H Sitting heights are affected by gender CO OD Ho Sitting heights are affected by an interaction between gender and handedness H Sitting heights are not affected by an interaction between gender and handedness Determine the test statistic The test statistic is Round to two decimal places as needed Determine the P value The P value is Round to three decimal places as needed Determine the proper conclusion at the 0 05 significance level Choose the correct answer below Sitting Height Data Female Male Right Handed 856 879 874 786 898 945 908 901 913 947 Print Left Handed 870 857 886 845 811 1000 917 1031 914 978 Done OA Fail to reject Ho There is insufficient evidence to support the alternative hypothesis There appears to be an interaction between gender and handedness OB Reject Ho There is sufficient evidence to support the alternative hypothesis There appears to be an interaction between gender and handedness OC Fail to reject Ho There is insufficient evidence to support the alternative hypothesis There does not appear to be an interaction between gender and handedness X

A dentist causes the bit of a high speed drill to accelerate from an angular speed of 190 rad s to an angular speed of 322 rad s In the process the bit turns through 3 141 rad Assuming a constant angular acceleration how long did the drill take during this change Your Answer

Find the maximum value of the objective function z The corner points of the bounded feasible region are 3 0 and 0 0 0 4 O Maximum value of z is 55 3 Maximum value of z is 24 58 Maximum value of z is 3 O Maximum value of z is 16 5 10 3 3 3x 4y

A car rental agency rents 190 cars per day at a rate of 20 per day For each 1 increase in rate 5 fewer cars are rented At what rate should the cars be rented to produce the maximum income What is the maximum income The rental agency will earn a maximum income of when it charges per day

Rewrite the following system of equations in matrix form and solve it using X A 1b x 2y 5 2x y 6

To solve this system of linear equations The values b c d e f and g are b C Do some elementary row operations as according to Gauss Jordan elimination to arrive at d e 2x 3 0 zs 324 1 221 37 213 24 5 f IL 222 223 we looked at the augmented matrix consistent inconsistent 1 0 0 2 01 0 b 0 0 1 d 0 0 0 f 31 C e 9 022 0 001 3 1 2 3 2 0 1 5

1 Supposed we set M 2 5 8 3 7 9 If you execute the following R command what output do you expect to see is matrix M M 5 drop F TRUE 4 7 FALSE NA

13 13e 5 47 36 2 L sin 6t say sinh 7 t 1 26 27 3 cos64 5 singt Se ty

1 Give examples of ways to show that a proposition is false

Form the dual maximization problem Use X X2 and x3 as the variables and f as the function and use the simplex method to solve the minimization problem Assume that all variables are nonnegative Minimize g 16y 15y2 subject to the following Y1 y 100 2y1 y 2 140 6y 5y 2 580 Maximize f 16 S 15 subject to X1 X2 X3 0 The minimum value of the objective function is which occurs at y

Use the matrices below 39 D 18 0 8 G 7 11 F Perform the indicated operation FD

If g x x 5 x find the following a g 1 2 b g c g 0 1

10 Let z 8i and z2 2 3 2i Find the trigonometric form of each complex number a Find the product of z and 22 b Raise zi to the power of 3

Amazon com Inc AMZN is one of the largest Internet retailers in the world Netflix Inc NFLX provides digital streaming and DVD rentals in the United States Amazon and Netflix compete in streaming and digital services however Amazon also sells many other products through the Internet The sales and total assets in millions from recent financial statements were reported as follows for both companies Amazon Netflix Total revenues sales 135 987 8 831 Total assets Beginning of year End of year 64 747 10 203 83 402 13 587 a Which of these assets are used by Netflix Inc to generate revenu a DVD content library b Distribution centers c Streaming content library d Manufacturing plant 1 a and b 2 a and c 3 a and d 4 b and c b Compute the asset turnover ratio for each company Round to two decimal places Amazon Netflix Asset turnover ratio c Which company generate sales

her W below is a mine the dimension of the subspace W A I2 13 subspace of R If it is a subsp o R 3x 2x2 13

1 15 pts Let 3 b b a Show that B is a basis for R L 1 2

0 1 with characteristic polynomial 6 20 pts Consider the matrix A x 1 a Find the eigenvalues of matrix A with their multiplicities b Find a basis for each eigenspace 1 2

1 15 pts Let 6 b b 2 3 2 2 a Show that B is a basis for R2

0 b Find a basis for each eigenspace 0 6 20 pts Consider the matrix A x 1 a Find the eigenvalues of matrix A with their multiplicities 0 1 1 2 with characteristic polynomial

1 Determine the whether the incated set of linearly independent complex vectors are 8 dependent 1 2i 96 2 1 1

7 0 8 5 3 0 5 15 pts Find the characteristic polynomial of the matrix A 9 5 use it to find eigenvalues of A Determine the multiplicities of the eigenvalues and

Let F 42 y 8y z 3z x F Use Stokes Theorem to evaluate F dr where C is the triangle with vertices 2 0 0 0 2 0 and 0 0 2 oriented counterclockwise as viewed f above

N 3 1 0 2 2 3 Vertex type your answer Bewer 4 Shift to the right 2 units reflect about the x axis vertical stretch by a factor of 2 and shift up 5 units Shift to the right 2 units reflect about the x axis vertical shrink by a factor of 2 and shift up 5 unit Shift to the left 2 units reflect about the Identify the vertex a the transformations with respect to the parent function of y z and write the equation of the quadrati vertical stretch by a factor of 2 and shift up 5 unit choose your answer type your answer 6 a type your answer Transformations www Mik HAN TOUR f x

Develop an amortization schedule for the loan described Round your answers to the nearest cent 90 000 for 3 years at 11 compounded annually Payment Interest Period 1 2 3 Balance Reduction Unpaid Balance 90 000 0 00

2 2i i 1 i Let A 2 2i i 1 i 2 4i 21 1 2i 1 A 10 be a matrix with eigenvalues 0 1 and i 2 It is known that there are many values of k such that A A Provide 3 different positive values of k that will allow for A A

Resolve the vector given in the indicated figure into its x component and y component A 0 4 0 A 6057 230 0 Q X

More on Polynomials Question 8 Which statement is true about the function shown here Select one This function is even This function is neither even nor odd This function is odd CIt is impossible to tell whether this function is even or odd This function is both even and odd 2

Use the shooting method to approximate the solution of the boundary value problem y 4y cos x y 0 0 y 0 with a step size h A 12 Let the first guess 0 0 and the second guess 0 1 0 117 Mamtal

The data shows the power generated by a wind turbine The x column gives the wind speed in meters per second The y column gives the power generated in kilowatts 3 4 7 NO 17 29 27 44 40 56 58 32 a What is the first differences of the y values b What are the second differences of the y values c When are the differences constant

in lottery requires players to select 8 different numbers in any order from 1 to 46 inclusive How many different sets of 8 number numbers can be chosen in different ways fy your answer Type an integer or a fraction CITOS

a 7C b 7P2 a 7C 21 Simplify your answer b 7P2 Simplify your answer

A bank offers a CD that pays a simple interest rate of 2 5 How much 2500 for a home entertainment center in 6 years The present value that must be invested to get 2500 after 6 years at an interest rate of 2 5 is Round up to the nearest cent

an automated teller machine at a certain bank you must enter a 6 digit code using the digits U 9 possible codes XX

Identify the patter in the list of numbers Then use this pattern to find the next number 4 7 11 18 29 47 82

3 Kate is planning on going to the pool a lot this summer It costs 5 to go each time but Kate noticed that the pool also offers a Summer Discount Card and a Summer Flat Rate Card The Discount card costs 50 but would allow her to go to the pool for only 2 each time The Flat Rate card costs 200 but would let her in to the pool for free all summer a What factors will be most important when Kate is deciding to buy the Discount card the Flat Rate card or neither b Write an equation for each of the three scenarios Explain your thinking c Graph your equations in a graphing utility or in a calculator What does the x axis represent What does the y axis represent d What do the intersection points of the lines represent e Decide which plan you think is the best and explain why

8 1 point What is the equation of the graph a y x 2 3 b y x 2 3 X A 20 12 c y x 2 3 d y x 2 3

CTIONL HApplication Directions For each of the questions in this section write your answers in the spaces provided Show all the steps 17 4 points Household smoke detectors contain 200 g of a radioactive element that has a half life of 432 years To the nearest g how much of this element will remain after 20 years Model Substitution Solve

Step 1 We want to maximize the function f 6x 7y subject to x ys 11 2x y 18 y 6 We start by graphing the feasible region given by the set of inequalities Thus we graph the equations x y 11 2x y 18 and y 6 as Select all of the given inequalities so the solution of the constraint system is the region on or Select the lines in the first quadrant since x 0 y 0 0 Select lines Notice that the test pc satisfies does not satisfy 20 19 18 47 16 15 14 13 12 11 10 9 No Solution y 6 x 0 y 0 8 7 6 S Fill Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties

2 In each case determine whether H is a subgroup of the group R R 0 a H 1 1 b H the set of all positive real numbers c H the set of all positive integers d H a b 3 R a b Q

A 3 1 2 4 25 1 6 3 1 a basket method 6 Minors and Cofactors

An arrow is launched upward with a velocity of 320 feet per second from the top of a 50 foot structure What is the maximum height attained by the arrow height function 4

Use the tips dataset Output the first 5 records of the Dataframe Then create one or more Python lines to calculate the average total bill for male smokers and show the output which would be the column name total bill and a number

Step 1 The solution of the system can be found using the Gauss Jordan elimination Recall that when using Gauss Jordan elimination the end goal is to obtain an identity matrix for the coefficien matrix by using elementary row operations Notice column 1 already has a 1 and then 2 zeros So next we focus on obtaining a 1 in row 2 column 2 This can be achieved by adding row 3 to row 2 and putting the result in row 2 1133 0419 0 360 H 20 3 1 1 3 37 179 0 360 0 Step 2 Next we focus on column 2 to obtain zeros in the first and third row entries To get a 0 in row 1 column 2 we can add 1 times row 2 to row 1 and put the result in row 1 Also to get a 0 in row 3 column 2 we can add 3 3 times row 2 to row 3 and put the result in row 3 10 4 01 LO O Submit Skip you cannot come mil 79 7 27 27 7 6 9 9 27 Step 3 Now we want to obtain a 1 in the third row last column To do this we need to multiply row 3 by 10 4 6 10 6 01 7 9 01 9 0 0 27 27 00 and put the result in row 3

A person wants to invest 14 000 for 2 years and is considering two different investments The irst investment a money market fund pays a guaranteed 6 7 interest compounded daily The second investment a treasury note pays 6 9 annual interest Which investment pays the mo interest over the 2 year period Select the correct choice below and if necessary fill in any answer box es to complete your choice Do not round until the final answer Then round to the nearest cent as needed OA The market fund is the better investiment since the market fund produces in interest and the treasury note pays R The treasury note is the better investment since the market fund produce in interest and the treasury note pays OC Both the market fund and the treasury note produce the same interest with in interest in interest 201 nsider intere any ar neares the ma e the ma

Which equation describes the line that passes through the giver points on the graph Select one y 5 a y x 3 c y b y 4x 1 3x d y x 1 5 H

find the absolute extremum with in the specked Minimum off x x 2x 3x 4 35 option A 2 61 B 2 62 C 2 62 J C 61

not get credit 5pts Solve the following Euler equation 7ry 9y 0 with initial conditions y 1 1 and 1 5 5pts For the same equation find a power series solution centered at To 1 with initial conditions y 1 7 and y 1 9 Give a recursion relation of its general coefficients and then calculate these coefficients up to degree four