Linear Algebra Questions and Answers

Find C11 and 22 where C 2A 3B A a C11 4 1 1 1 and 3 7 B 5 3 2 0 5 b C22

1 In 2004 the restaurant industry in the United States employed about 11 9 million people In 2014 this number increased to 13 5 million employees a Find a linear function E that models these data where x is the year I b Interpret the slope of the function E x Attach the units c If this trend continues use your equation to predict the year that the number of restaurant industry employees might reach 14 5 million

4 6 points A 4 0 and B 1 2 2 Find X if 2X 2A B I

8 Sketch a graph of the following function Be sure to include all asymptotes increasing and decreasing intervals and max and min You do not have to find any concavity or points of inflection y x 1 3 KU 2 A 2 C 2T 2

18 Find the intersection if any and provide a geometric interpretation of the A 3 following three plane systems x y 2z 2 0 3x y 147 6 0

11 For what values of x does the function y xe x have maximum or min values A 2 T 2

A nut store normally sells cashews for 4 00 per pound and peanuts for 1 50 per pound But at the end of the month the peanuts had not sold well so in order to sell 90 pounds of peanuts th manager decided to mix the 90 pounds of peanuts with some cashews and sell the mixture for 2 50 per pound How many pounds of cashews should be mixed with the peanuts to ensure no change in the revenue

Find the values of x that satisfy the inequality 1 8 Ox 11 x 88 X 1 00 11 x 11 Ox 88 X

of a sports car will cost 3 2 less than the current model The current model costs 31 000 How much will the price decrease in dollars Wha will be the price of the next model Decrease in price Price of next model

Review Course Packet on factoring techniques Simplify the expression by first pulling out any common factors in the numerator 1 x 2 6 4x 6 1 x 4x 1 x2 4

2 nts 01 27 23 The dashboard shows a company s beginning inventory along with its merchandise purchases and merchandise sales for the period Beginning of Year During the Year During the Year 0 Inventory 110 50 Required A Required B Merchandise Purchases 270 Merchandise Sales 290 100 Enter answers for each of the following 150 200 250 Help A physical count of inventory at year end shows 85 of inventory exists Prepare the journal entry to record inventory shrinkage Save Ex

Match the expression on the left with its simplified form on the right Answer options on the right may be used more than once 1 31 1 31 131 131 3

7 The market for college athletes Suppose that Sam an excellent high school basketball player is being recruited by the University of California Berkeley that is Berkeley is the consumer In this example NCAA rules prevent universities from compensating student athletes more than the full cost of tuition Assume that recruiting for college athletes is organized under a perfectly competitive environment The following graph shows the supply of and demand for Sam s athletic services Suppose that Berkeley s annual tuition is 33 000 the amount scholarship money or the wage Sam receives in exchange for playing at Berkeley Shade the area representing Berkeley s consumers surplus using the green point triangle symbol Then shade the area representing Sam s total wage revenue using the purple point diamond symbol 60 WAGE Thousands of dollars 54 46 42 36 30 Demand 24 18 12 Tuition Sam s Athletic Services Supply A CS Total Wage

3 Find a homogeneous linear system with two equations that are not multiples of one another and such that and x 1 X 1 X3 1 X4 2 x 2 X 0 X3 3 x4 1 are solutions of the system

5 Aidan and his sister Ella are having a race Aidan runs at a rate of 10 feet per second Ella runs at a rate of 6 feet per second Since Ella is younger Aidan is letting her begin 30 feet ahead of the starting line Let y represent the distance from the starting line and x represent the time elapsed in seconds Write an equation to model the distance Aidan traveled Write an equation to model the distance Ella traveled Exactly how many seconds does it take Aidan to catch up to Ella Justify your answer

How expensive is Maui A newspaper gave the following costs in dollars per day for a random sample of condominiums located throughout the island of Maui 88 50 66 60 360 55 500 71 41 350 60 50 240 45 45 125 235 LUSE SALT a Compute the mean median and mode for the data What is the mean What is the median 65 60 What is the mode 120 b Compute a 5 trimmed mean for the data and compare it with the mean computed in part a Round your answer to two decimal places Does the trimmed mean more accurately reflect the general level of the daily rental costs Yes the trimmed mean is closer to the median and mode Yes the trimmed mean is further from the median and mode No the trimmed mean is further from the median and mode No the trimmed mean is closer to the median and mode c If you were a travel agent and a client asked about the daily cost of renting a condominium on Maui what average would you use Explain The Select seems to represent the costs most accurately since Select should be the one reported Is there any other information about the costs that you think might be useful such as the spread of the costs No other information about condominium costs would be useful The lowest and highest prices of the condominiums would also be useful The average price of a condominium in 1980 would also be useful so it

A marginal change and a point on the line y a bx are given b 1 09 x y 2 76 4 a Determine the y intercept 0 a C x y b Write an equation of the line in statistical form

Write the statistical form of the line having the given slope and y intercept Let x be the independent variable and y be the dependent variable marginal change is 28 25 y intercept is at 9 17

The solution of the following system x 2y 2x 5 x y 3 is O a None O b 6 1 O c No solution O d 1 2 O e 9 4

ex if A is uxn matrix Find conditions such that det A det A

Graph the line with slope b 1 5 passing through 0 3 3 10 10 5 5 10 5 10 10 5 5 10 5 2 6 3 0 3 3 5 10 X X 10 7 2 6 3 10 5 5 10 10 0 3 3 10 4 3 0 334 5 5 10 10 X

following table O Research Paper Score Construct a scatterplot of the data in which the horizontal axis corresponds to the midterm score and the values start at 65 and end at 100 and the vertical axis corresponds to the research paper score and the values start at 66 and end at 88 Research Paper Score 88 86 84 82 80 78 76 74 72 70 68 66 Midterm Score 70 90 85 82 96 65 95 88 86 84 82 80 78 76 74 72 70 68 66 Research Paper Score 68 66 71 78 81 84 73 65 70 75 80 85 90 95 100 Midterm Score 65 70 75 80 85 90 95 100 Midterm Score Research Paper Score Research Paper Score 88 86 84 82 80 78 76 74 72 70 68 66 88 86 84 82 80 78 76 74 72 70 68 66 65 70 75 80 85 90 95 100 Midterm Score 65 70 75 80 85 90 95 100 Midterm Score e

Plot the point on the rectangular coordinate system B 3 7 BO L 8 6 4 2 8 6 4 2 II III IV 8 6 4 2 N 4 6 8 8 6 4 2 2 4 8 2 468 2 4 6 8 Specify the quadrant in which the point lies if any 8 6 4 2 B LLL 8 6 4 2 6 4 2 2 4 9 an 00 6 4 2 2 4 166 00 2 2 4 if B 4 6 8 6 8 X

Use the time series plot to answer the question Average Price of Residential Natural Gas in dollars per million Btu 15 14 0 8 01 4 5 6 7 3 Number of Years Since 2000 During how many years from 2000 to 2010 was the average price of natural gas less than 12 per 1 million Bt 9 10

Determine the intercepts of y 12 2x x intercept x y y intercept x y Use the intercepts to graph the linear equation No Solution 14 12 10 4 4 2 14 42 40 a 6 4 2 2 4 10 12 2 4 6 4 10 12 14 U Fill Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties

Example 1 Let a function f be represented symbolically by f x x 1 a Evaluate f 2 f 1 and f a 1 b Find the domain off

our different linear functions are represented below 10 8 6 Function 1 105 Function 3 y 4x 1 Answer the following questions 10 Function Function 2 Function X 2 1 0 1 2 a Which functions have graphs with slopes less than 3 Check all that apply Function 1 Function 2 Function 3 Function 4 y 3 4 5 6 7 Function 4 The slope is 5 and the y intercept is 4 b Which function has the graph with the greatest y intercept Function 1 Function 2 Function 3 Function 4 c Which function has the graph with a y intercept closest to 0 Function 3 Function 4

1 Compute the following limits using graph of f x 4pts 3 2 H F 3 H 1 2 3 a lim f x X 3 b Jim X 2 x c lim x c lim f x X 0 d lim f x X 2

Where does all the water go According to the Environmental Protection Agency EPA in a typical wetland environment 38 of the water is outflow 47 is seepage 7 evaporates and 8 remains as water volume in the ecosystem Chloride compounds as residuals from residential areas are a problem for wetlands Suppose that in a particular wetland environment the following concentrations mg L of chloride compounds were found outflow 74 0 seepage 75 7 remaining due to evaporation 50 2 in the water volume 70 6 a Compute the weighted average of chlorine compound concentration mg L for this ecological system Round your answer to one decimal place x mg L

Consider the following formula x 50 S n Evaluate this expression using the given values Round the result to two decim x 50 7 s 6 3 n 27

Simplify the expression Round your answer to three decimal place 10 2 3 20 2 12 30 2 6 3 12 6

Simplify the expression 10 9 8 4 3 2

Classify 1 645 expression variables X 42 5 9 7 O equation Identify the variables coefficients and constants Enter your answers as a comma separated list If there is no answer enter NONE coefficients as an algebraic expression or an equation

Consider the following points 2 4 4 8 6 12 a Determine the polynomial function of least degree whose graph passes through the given points p x 2x 12x 24

Classify 1 645 variables expression equation Identify the variables coefficients and constants Enter your answers as a comma separated list If there is no answer enter NONE coefficients Xx 44 5 9 1 constants as an algebraic expression or an equation

Evaluate the following expressions a 4 5 3 23 5 b 6 x 6 5 2 4 Question 5 of 8 11

The monthly cost in dollars of water use is a linear function of the amount of water used in hundreds of cubic feet HCF The cost for using 14 HCF of water is 33 53 and the cost for using 25 HCF is 51 68 What is the cost for using 16 HCF of water Monthly cost in dollars Water usage in HCF

Factor fully 11 x 3 y x 3 o 11 y x 3 o 11 y x 3 o y 3 x 11 o y 11 x 3

Factor fully 112x 150x27 8x 3 14x 9 o 8x 9 14x 3 o 8x 9 14x 3 O 9x 8 3x 14

Choose the simplified form 3x 4 4x 2 3 7 o 12x2 10x 10 O 9x 10x 13 O 9x 10x 13 12r2 70

Given the expression 9 3x 4 4y x y 1

ab 2a 3b a 8b 6ab 3b 4a ab O a 6ab 2b D a 6ab 26 O a 6ab2b O a 6ab 26

Solve the quadratic equations by completing the square Leave answers in exact form with radicals as needed Enter the answers in ascending order smaller value first Convert the square root to exponential form Example should be a x 8x 3 0 MART m and x

fully 77x y 88x y O x y 77y 88x O 11x y 7x 8y o 11x y 7y 8x o 11 7x y 8x y

you add the following polynomials what is the correct simplified form 2x 5xy 2 x Tru 6

Solve for x x 3x 28x 0 KE

Your company has a profit that is represented by the equation P 1 5x 24 where P is the profit in millions and x is the number of years starting in 2018 a Graph the relation b Is this relation linear quadratic or neither Explain your answer in two different ways c What is the direction of opening and does profit have a maximum or minimum How do you know d What is the P intercept of this relation What does it represent Do you think it would make sense that this is a new company given the P intercept Explain Task 2 Solving for break even point s A break even point for a company is when they are neither making nor losing money This is when the profit is P 0 a How many break even point s will there be What do you use to determine this b Determine in which year s the company will break even using any algebraic method you wish c Determine in which year s the company will break even using a different algebraic method than you chose in b d Which method the one you used for b or the one you used for c did you prefer Explain why Task 3 Determining different profits a In the year 2024 how much profit will the company be making Solve this algebraically

Solve the system using either Gaussian elimination with back substitution or Gauss Jordan elimination If there is no solution enter NO SOLUTION If the system has an infinite number of solutions express x and y in terms of the parameter t 3x 12y 15 3x 12y 15 x y 1 s t X

Solve the system using either Gaussian elimination with back substitution or Gauss Jordan elimination If there is solution enter NO SOLUTION If there are an infinite number of solutions set x3 t and solve for X and X X1 3x1 x 2x3 2x 2x X3 3x3 1 7 4 X1 X2 X3

Solve the system using either Gaussian elimination with back substitution or Gauss Jordan elimination If there is no solution enter NO SOLUTION If the system has an infinite number of solutions express x and y in terms of the parameter t x y 3x 12y 15 3x 12y 15