Linear Algebra Questions and Answers

Use the fundamental counting principle The students in the 17 member advanced communications design class at Center City Community College are submitting a project to a national competition They must select a 5 member team to attend the competition The team must have a team leader and a main presenter the other 3 members have no particularly defined roles In how many different ways can this team be formed There are ways the team can be formed Simplify your answer Type a whole number

JV Level a warm up A snack bar cooks and sells hamburgers and hot dogs during football games 3 To stay in business it must sell at least 10 hamburgers but cannot cook more than 40 b It must also sell at least 30 hot dogs but cannot cook more than 70 c The snack bar cannot cook more than 90 items total d The profit on a hamburger is 0 33 and on a hot dog it s 0 21 How many of each item should the snack bar sell to make the maximum profit Variables X number of hamburgers sold 7 Hot dogs sold Constraints Objective Functions Graph Table 10 x 40 30 y 70 10 0 int 0 90 Tatal item b XtY290

1 point Find the determinant of the matrix M M 1 2 2x x3 10 6x 6 2x 4x 1 x 2x and use the adjoint method to find M det M 20 12x 1888 0 0 3 3x

Results for this submission Entered 12 13 5 18 The answer above is NOT correct Answer Preview 12 13 5 18 Result incorrect Find the point P such that v PQ has the components 9 9 25 13 Q 3 4 25 5 P help points YOL

At noon ship A is 170 km west of ship B Ship A is sailing east at 40 km h and ship B is sailing north at 20 km h How fast in km hr is the distance between the ships changing at 4 00 p m Round your answer to three decimal places km h

Complete the following truth table p q v q Pq 0 0 01 10 11 G 94 S FI

class we conside optimizing can Square MSE practice ther are other choices of loss functions as well For this problem we will consider linear regression using Mean Absolute Error MAE as our loss function Specifically the MAE loss is given as JMAE 0 Solution a 4 points Derive the partial derivative JMAE 0 30 otherwise Solution OJMAE 0 20 Hint For this question you don t need to worry about J 0 You can use the sign function 1 2 y s t sign y n 76 n 0 x i y i i 1 VOJMAE 0 1 20 n 81 30 n sign 0 x y x sign 0x y 0 x i y i 1 1 0Tx y b 2 points Write the vectorized solution for the gradient of the loss function i e VeJMAE 0 Solution n sign Tx y i x c 4 points Given the following dataset of 8 points what is the value of of JMAE 0 and JMSE 0 at 0 1 0 1 0 1 0 How about their gradients VJMAE 0 and VoJMSE 0 1 i 1 2 5 3 24 0 1 1 0 1 2 2 2 1 12 3 1 6 3 JMAR A 3 375 IMSE A 10 3125 6 7 8 1 0 5 2 3 0 6 8 7

The heights of male Great Danes have a mean of 34 inches with a standard deviation of 1 5 inches A random sample of 100 Great Danes have a sample mean of 34 2 inches What is n What is A What is the standard deviation of the sample means OTT What is A A What is the probability of a sample mean the is more than 34 2 inches Round your answer to 3 decimal places

Question 7 7 6 5 4 3 2 1 Graph the transformation of f x 6 Then give the horizontal asymptote the domain and the range f x 6 Clear All Draw Horizontal asymptote y 6 5 4 3 2 H 4 2 3 4 5 6 7 y 12 3 4 5 X 6 7

3 Paul and Polly sell lemonade in front of their house in the summer During the month of June they sold about 26 cups of lemonade a day at a price of 0 50 per cup In July they plan to increase their cups sold by 2 cups every day with some clever new advertising They will also decrease the price per cup by 1 cent every day Write an equation for a function L d that gives the amount of money Paul and Polly make selling lemonade on day d in July

For the encoding matrix T 14 2 3 A 38 7 7 41 7 8 decode the message 57 166 1 4 11 175 27 which gives a six character word

In each part find the matrix X solving the given equation OC a b C 4 6 1x 82 X 0 8 Jx 43 X 3 6 1 10 1 9 7 X X X

Questions 1 and 2 are about the following graph G 9 13 10 11 12 15 16 Question 1 Find a Hamilton cycle in G or write NO if one does not exist Question 2 What is the smallest number of edges adding which makes G Eulerian Question 3 Find a simple formula not involving for 4 AC n

A total of four shows when we roll two fair dice a Find the probability of the given event b Find the odds against the given event a The probability of the given event is Simplify your answer Type an integer or a simplified fraction

Congress has the power to collect taxes President has the power to make treaties Principle of checks and balances incorporated B The bulleted list above is in response to issues that arose under the Three Fifths Compromise Declaration of Independence Articles of Confederation

9 Write the equation of a rational function g x that satisfies ALL of the criteria below The graph of g has an z intercept at z 2 The graph of g has a vertical asymptote at z 1 4 The graph of g has a horizontal asymptote at y 3 The graph of g has a hole at z 6

Use PMT nt to determine the regular payment amount rounded to the nearest dollar The price of a small cabin is 1 1 1 30 000 The bank requires a 5 down payment The buyer is offered two mortgage options 20 year fixed at 7 5 or 30 year fixed at 7 5 Calculate the amount of interest paid for each option How much does the buyer save in interest with the 20 year option Find the monthly payment for the 20 year option Round to the nearest dollar as needed

Plastic Hanging Display Strips with hooks Product Display clips for reta

Find the domain of the following function f x 1 4x

24 Suppose the current cost of gasoline is 3 22 per gallon Find the current price index using the 1975 24 price as the reference value In 1975 the cost of gasoline was 56 7 cents per gallon A 265 3 B 5 7 C 17 6 D 567 9 25 Suppose the current cost of gasoline is 3 28 per gallon Find the current price index using the 1995 price as the reference value In 1995 the cost of gasoline was 120 5 cents per gallon A 2 7 B 272 2 C 207 5 D 36 7 25

0 047619 0 952381 5 1 U1 At least one of the answers above is NOT correct v 1 20 21 21 5 1 and incorrect incorrect Find two vectors and 2 whose sum is 5 1 where is parallel to 5 4 while 72 is perpendicular to 5 4 The first coordinate is incorrect The second coordinate is incorrect The first coordinate is incorrect The second coordinate is incorrect

Consider the amount of simple interest earned 1 000 at 7 for 6 years Give the formula for simple interest where I is the interest in dollars P is the present value in dollars r is the annual interest rate as a decimal and t is the time in years I p r t 100 Determine the following values P 1000 r 0 07 t 6 1000 7 6 100 p r t 100 Calculate the amount of simple interest earned 420 Need Help Read It X Your answer cannot be understood or graded More Information

1 point Let a 3 4 3 and b 2 1 4 Show that there are scalars s and t so that sa tb 8 14 20 You might want to sketch the vectors to get some intuition S II

Let A 2 2 11 2 3 2 2 3 a Find the determinant of A det 4 3 b Find the matrix of cofactors of A adj A c Find the adjoint of A A A d Find the inverse of A 00

assign6 Problem 9 1 point A and B are n x n matrices Check the true statements below A If det A is zero then two rows or two columns are the same or a row or a column is zero B If two row interchanges are made in succession then the determinant of the new matrix is equal to the determinant of the original matriz C The determinant of A is the product of the diagonal entries in A D det AT 1 det A

If then uu 0 and uu U

12 of 15 Macmillan R x and S x are rational functions then R x S x is after common factors are canceled also a rational function Suppose the vertical asymptotes of R x are x 1 and x 4 and that the only vertical asymptote of Six is x2 What are the vertical asymptotes of R x S x Give your answer as a comma separated list of equations if needed Express numbers in exact form Use symbolic notation and fractions where needed Enter DNE if fonction has no vertical asymptotes vertical asymptotels of R S

To 0 17 f 0 1 0 X 4 8 1 X 0 0 9 1 47 4 3 6 8 9

3 d Suppose that E4 2 2 Find E4 and E E4 E e Suppose that E5 Find E5 and E5 E5 5 1 5 2 4 3 5 1 2 5 2 2 4 1 ser 2255914 22 3 5 1 8 20 8 2 4 3 5 1 4 1 5 2

a Suppose that E 1 88 E b Suppose that E2 89 E2 E3 c Suppose that E3 T 8 E 5 Ez 3 4 25 11 Find E2 and E 12 27 Find E and E 8 Find E3 and E

1 point Write X E 3 1 9 9 as a product X E E2 E3 of elementary matrices E2 291 E3 29

Assignme 1 point Problem 27 a Find the inverse of the matrix A A b Use the answer from part a to solve the linear system 5x1 3x 1 5 10 397 5 21 2 8 888 3 1 10x2 39x3 5x2 21x3 2x2 8x3 A 18 2 3 4

f Suppose that E6 ge qc ca webwork2 105zahrai Assignment4 1 effectiveUser 2255914 Find 6 and 6 00 000 00 E6 E 1 3 2 2 5 1 5 2 4 1 3 5 2 19 11 5 2 31 6

1 point Let E be the 3 x 3 matrix that corresponds to the row operation R3 R3 3R a Find E 25 39 157 b Find EA where A 34 20 18 39 31 19 E

1 point Solve for X 29 0 X em 23 2 3 X 3 8 5 7 5

1 point E Assume that A is a matrix with four rows Find the elementary matrix E such that E A gives the matrix resulting from A after the given row operation is performed Then find E and give the elementary row operation corresponding to E 6R3 R3 E 1 ment DE D Problem 7 L The elementary row operation corresponding to E is O A R3 R2 R3 OB R3 R3 OC R R

In each part find the matrix X solving the given equation 171x X a b 1 J x X C d e 4 f 4 17 1 0 0 1 0 X X X 0 COO 0 X 6 3 8 9 9 4 X X X 0 0 1 0 1 0 X 4 3 1 00 8 82 8 2 9 2 4 4 X ak 9 1 4 6

point en A A 4 21 0 0 1 5 0 0 0 0 1 5 3 16 000

1 point Give a 3 x 3 elementary matrix E which will carry out the row operation R R3 E 000 Test that E actually works for carrying out this row operation by computing the product EA for the matrix 1553 2 4 11 5 15 24 1531 2 EA 0000 A Note In order to get credit for this problem all answers must be corrent

en A A 1 0 0 07 5100 5 5 10 9 7 1 1 00

Assignment4 Problem 12 1 point The inverse of the matrix is where b11 b12 b21 b22 Note You can A A 3 6 b11 b12 b21 b22

1 point Consider the following two systems a b 2x y 1 x y i Find the inverse of the common coefficient matrix of the two systems system a and B Solution to system a x Solution to system b x for system b 2 3 E 1 2x y 1 x y 2 ii Find the solutions to the two systems by using the inverse i e by evaluating A B where B represents the right hand side i e B 1 881 23 2

1 point Select all statements below which are true for all invertible n x n matrices A and B OA A In is invertible OB In A In A In A Oc A B A B A B OD A is invertible

Assignment4 Problem 26 1 point Find the inverse of the matrix The inverse is 1 2 27 44 A 0 1 1 3 0 0 A 2

1 point Find the inverse of AB if 1 4 4 2 83 4 3 0 4 A 1 and B AB 001

Let Then where a11 a13 921 0 a12 a22 Preview My Answers Submit Answers A A 1 a23 1 1 Note In order to get credit for this problem all answers must be correct 2 0 28 9 5 a11 a12 a13 a21 a22 a23 a31 a32 a33 0 931 0 a a32 a33

Solve the system of equations 3x 6y z 5 x y z 1 x 2y 2 by converting to a matrix equation and using the inverse of the coefficient matrix x

Find the complex zeros of the quadratic function h x x 12x 52 O 6 41 6 4i 6 41 6 16i 6 16i 10 2

5 i is a zero of a quadratic equation with real coefficients Find the other zero 5 i 5 i 5 i 5 i

An enviromentalist wants to determine the relationship between the numbers in thousands of forest fires over the yaer and the number in hundred thousands of acres burned The data for 8 recent years are shown Determine if the relationship is linear by finding the linear correlation coefficient Round your answer to two decimal places Number of fires x Number of acers burned y 72 62 0 84 1 32 69 47 84 0 77 58 62 57 45 0 90 42 19 26 51 15 30 15