Linear Algebra Questions and Answers

given Find is to rasie demand function D P 100 4p at the the elasticity of demand price of 2 a the demand elastic inclastic or unitary revenue do lower prices you of kee prices unchanged increase prices

Find a basis B for the span of the given vectors HOO B 0 0

Find the determinant assuming that a b de f 3 ghi 6a b 7 c 6d e 7 f 6g h 7

Let TA R2 R2 be the matrix transformation corresponding to A Find T u and TA V where u u TA V 3 2 and v 2 00 00 3 4 2 1

The following function is one to one Find the inverse algel

nected graph is shown Identify the follow dges ops elect the correct choice below and if nece ce A Edge s is are a bridge s Use a comma to separate answers a B There are no bridges in the given grap

Units of capital K 150 100 75 50 25 4 09 25 q 1001 9 200 50 75 Units of labor L The above graph shows a firm s isoquants and isocost curves 9 300 100 150 1 Assume that the price per unit of capital r is 4 and the price per unit of labor w is 4 as well What is the total minimum cost of producing 200 units 2 What condition has to be fulfilled for the firm to produce with a cost minimizing combination of capital and labor Please circle all correct answers a The marginal product of labor MPL has to be equal to zero b The marginal product of capital MPK should be equal to the marginal product of labor MPL c The marginal rate of technical substitution w r d MPL w MPK r

The vector field F x y x y represents an ocean current An iceberg is at the point 1 2 at t 0 Determine the position of the iceberg at time t 4 ae ced where a i b i C d i

Speedometer readings for a vehicle in motion at 6 second intervals are given in the table 12 t sec 0 6 18 24 30 36 v ft s 0 9 33 59 75 72 53 Estimate the distance traveled by the vehicle during this 36 second period using L6 and R6 L6 RG feet

In Exercises 27 34 if possible find AB and state the order of the result 27 A 28 A 2 3 1 30 A 1 6 To 29 A 4 8 1 31 A 0 0 13 1 0 1 6 040 1 4 5 0 3 352 5 0 32 A 0 8 0 0 B 4 3 01 2 7 8 17 0 DON o 1 0 0 0 2 B 1 6 0 0 7 1 8 31 B B 2 3 3 B 0 0 10010 B 0 9271 4 4 1 6 7 0 0 0 5 1 0 2 00110

0 33 A 0 0 34 A 10 12 in a 0 0 3 0 4 6 11 B 8 16 0 0 B 6 2 1 6 4 4 0

Let 9 A 2 25 4 Find an invertible matrix C and a diagonal matrix D such that A CDC C 188

Find two consecutive odd integers such that the square of the first added to 3 times the second is 34 The numbers are and

Let P Find p p 0 5 0 1 0 5 0 9 18 be the transition matrix for a Markov chain with two states What proportion of the state 2 population will be in state 2 after two steps

Suppose that the weather in a particular region behaves according to a Markov chain Specifically suppose that the probability that tomorrow will be a wet day is 0 666 if today is wet 0 250 if today is dry The probability that tomorrow will be a dry day is 0 750 if today is dry and 0 334 if today is wet a Write down the transition matrix for this Markov chain Order the rows and columns by dry first then wet 183 b If Monday is a dry day what is the probability that Wednesday will be wet c In the long run what will the distribution of wet and dry days be Round your answers to one decimal place In the long run about will be wet of the days will be dry and

Let T R2 R2 be the matrix transformation corresponding to A 3 2 Find TA u and TA V where u u TA V 11 00 00 1 2 3 2 and v 4 1

Let P 0 5 0 3 0 5 0 7 X be the transition matrix for a Markov chain with two states Let xo Find the steady state vector x Give the steady state vector as a probability vector 18 be the initial state vector for the population

Show that v is an eigenvector of A and find the corresponding eigenvalue 1 0 1 1 BH0 A 1 1 2 1 3 3 1 1

58 For each pair of intercepts given below write an equation for a quadratic function in standard form 3 0 and 2 0 a b 3 0 and 0

Let P p 1 2 3 000 0 3 1 2 3 3 2 3 be the transition matrix for a Markov chain with three states Find p 0 What proportion of the state 2 population will be in state 3 after two steps

Let TA R R be the matrix transformation corresponding to A 1 TA u TA V R 2 Find TA u and T v where u 3 3 2 and v 2 2

Show that the given transformation from R2 to R2 is linear by showing that it is a matrix transformation F reflects a vector in the y axis Reflecting a vector in the y axis means negating the x coordinate So 1 1 F1 9 13 and thus F is a matrix transformation with matrix F 8 It follows that F is a linear transformation

Let P 0 5 0 9 0 5 0 1 x be the transition matrix for a Markov chain with two states Let x Compute x and X 0 5 0 5 be the initial state vector for the popula

Find the standard matrix of the given linear transformation from R2 to R Projection onto the line y 8x

5 9 of the students in a Biology class passed a Biology test If these students are 60 of all the students in the class how many students are in this Biology class Round your answer to the nearest whole number if necessary 24

There were 1125 books sold last week at Sid s Bookstore The circle graph below summarizes these books by genre The central angle for the Mystery slice is 103 68 What percentage of the books sold were Mystery books Do not round Romance Self Help Mystery 103 68 Cooking Biography X

3 Consider the following matrix A 1 0 1 0 a Calculate all of the eigenvalues of A b For each eigenvalue of A found in a find a basis for the corresponding eigenspace c Determine whether the collection of all basis vectors found in b is linearly depend or linearly independent d Is the matrix A diagonalizable Explain why or why not

8 A mass weighing 16 pounds stretches a spring feet The mass is initially released from rest from a point 3 feet below the equilibrium position and the subsequent motion takes place in a medium that offers a 3 1 the instantaneous velocity Find the equation of motion x t if the mass is driven by an external force equal to f t 10 cos 3t Use g 32 ft s2 for the acceleration damping force that is numerically equal to 2 due to gravity x t ft

Solve the given initial value problem d x 4x 2 sin 2t 4 cos 2t x 0 1 x 0 1 dt x t

A 1 kilogram mass is attached to a spring whose constant is 24 N m and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 11 times the instantaneous velocity Determine the equations of motion if the following is true a the mass is initially released from rest from a point 1 meter below the equilibrium position 3 x t 5e 8t 8 3t 5e m b the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 11 m s x t m hs

or the following table compute the area of a 520 square foot shed left to paint if y Start of Day Area L 1 2 3 4 5 Complete the table Start of Day 1 2 3 4 5 What kind of decay is this Area Left

Sarah Conrad earns 16 000 every month The social security wage base is 117 000 What will be Sarah s social security medicare tax deductions in the month of October

Find the transpose of the matrix 1 5 8 19 2 13 10 3 8 05 24 5 8 19 1 The transpose of 2 13 10 3 is 24 8 0 5

Only about 12 of all people can wiggle their ears Is this percent different for millionaires Of the 320 millionaires surveyed 48 could wiggle their ears What can be concluded at the a 0 10 level of significance a For this study we should use Select an answer b The null and alternative hypotheses would be Ho Select an answer H Select an answer please enter a decimal Please enter a decimal c The test statistic d The p value e The p value is a f Based on this we should Select an answer the null hypothesis g Thus the final conclusion is that please show your answer to 3 decimal places Please show your answer to 3 decimal places The data suggest the population proportion is not significantly different from 12 at a 0 10 so there is statistically insignificant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 12 The data suggest the populaton proportion is significantly different from 12 at a 0 10 so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 12 The data suggest the population proportion is not significantly different from 12 at a 0 10 so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is equal to 12

estion 7 6 5 4 3 4 7 Slope m 6 5 4 3 2 4 2 Find the slope of the line Ma 6 Enter your answer as an integer or as a reduced fraction in the form A B No deci

Multiply the monomial and the polynomial Assume any variable exponents represent whole numbers 2x5 9x6 12x 8 O A 18x 1 24x7 16x5 OB 18x 1 12x 8 O c 18x 1 24x7 O D 18x6 24x 16

Mei adjusts the launch angle and power and she switches the robot s units from feet to meters With these new parameters the ball s height y in meters and horizontal distance x in meters can be modeled by the equation below y 0 002x 0 23x 1 4 Use the graph or table feature of a graphing calculator What is the maximum height reached by the ball What is the horizontal distance the ball has traveled when it is at its maximum height Part D After another adjustment the tennis ball s height y in meters and horizontal distance x in meters can be modeled by the equation below y x 8x 6 Use the Quadratic Formula to find the exact horizontal distance the ball has traveled when it hits the ground Simplify your answer if possible and explain how reblom

Sterling Inc reports the following financial information for its sports clothing segment Average operating assets Controllable margin Minimum rate of return Return on investment Compute the return on investment and the residual income Residual income 3 059 000 672 980 10 96 96

Based on the graph find the set of all x values for which the points P x y ar Enter your answer using interval notation 1 7 6 5 4 3 2 1 1 2 3 4 5 The solution set is 2 3 on 5 6

A corporation creates a sinking fund in order to have 340 000 to replace some machinery in 8 years How much should be placed in this account at the end of each week if the annual interest rate is 6 2 compounded weekly Round your answers to the nearest cent 631 78 How much interest would they earn over the life of the account 77179 52 Determine the value of the fund after 2 4 and 6 years 2 years 3072 75 4 years 1441 22 6 years 900 23 x x How much interest was earned during the second week of the 4th year

Find the equation in terms of 2 of the line through the points 3 3 and 1 5 21

A poll of 3116 people revealed that of the respondents that were registered Republicans 826 approved of their representative job performance 409 did not and 734 had no opinion Of the registered Democrats 240 approved of their representative s jo performance 434 did not and 75 had no opinion Of those registered as Independents 118 approved 110 did not approve a 21 had no opinion Of the remaining respondents who were not registered 75 approved 47 did not approve and 27 had no opinion Represent these data in a 3 x 4 matrix Approved Disapproved No Opinion Republicans Democrats Independents Not Registered 00 0

A ring shaped region is shown below Its inner diameter is 30 in The width of the ring i 4 in

Solve by factoring 4 2x 11x 6 0 b x 4x 21

f 2 f 1 f 0 f 1 f 2 Question Help J x 3x Video 5x 7 Calculate the following values

nts DETAILS t the polar equation to rectangular coordinates 2 r 1 sin 8 d Help Read It

try Spring 2023 Sp23 MATH 1106 90 Tri 1 Points DETAILS Need Help onvert the equation to polar form Use variables y 2 Ass Read It

A data set includes wait times minutes for the Tower of Terror ride at Walt Disney World s Hollywood Studios theme park at 5 00 PM Using 37 of the times to test the claim that t mean of all such wait times is more than 30 minutes the accompanying Excel display is obtained Test the given claim by using the display provided from Excel Use a 0 05 significance level Click the icon to view the Excel display Identify the null and alternative hypotheses Ho C

Determine the y intercept and the slope for each of the linear relations represented below Label the y intercept on the graph Record the values in the right column Graph Key Features x y 211 18 05 12 2 1

14 of 15 Consider the polynomial function m x 6 5 4 6 15A J10 54 2 1 0 5 10 15 20 25 30 35 40 45 1 2 4 5 6 X x4 Part A 5x 36 whose graph is sh What are the linear factors of m Select all that apply x 3 x x 3 x 3i x 3i x 2 x 2 x 2i x 2i Part B What are the zeros of m Select all that apply 1 x 3 x 2 x 2 x 3 x 3i x 2i x 2i x 3i