Linear Algebra Questions and Answers

Given A 0 1 5 4 determine if x 1 1 0 is an eigenvector why or why not 2 9 0 2

3 Determine if T R R T x y z x 1 y 1 z 1 is a linear transformation

For full credit show all work and explain your answers 3 2 1 Illustrate 1 using the rectangular area model 4 916 II morld 2291 2redmun rbidw 992 of easbo ni novig e9lun ylilidieivib yllyt nislax3 02

4 5p Use Stokes Theorem to evaluate s curl F ds Suppose F x y z ycos z e sin z xe and S is the upper hemisphere of radius 3 orient upward

4a 10 pts Show that the following sequence of functions nx 2x is uniformly convergent on 0 1 and find Justify your answer TL lim 71 00 z 0 1 f fn 2 dx

Use a method to yield the eigenvalue with the largest absolute value of the following matrix 4 2 11 0 3 12 with Fo 1 1 4 Show results of the first two iterations 21

3 Use or to compare the two numbers 96 151 15 691

6 5 384 351 The 5 in the tens place is the value of the 5 in the millions place

Suppose that the temperature at a point x y on a metal plate is T x y 4x 4xy y An ant walking on the plate traverses a circle of radius 3 centered at the origin What are the highest and lowest temperatures encountered by the ant NOTE Enter exact answers Highest Temp Lowest Temp

0 Let A X a a2 9 b and B b with real entries such that A XB where 1 1 17 31 k x be two 2 x 1 matrices and k R If a a 3 b b and k 1 b2 2b b2 then the value of k is JEE Main 2021

Your patient is ordered 1 2 g m2 day to infuse for 120 minutes The patient is 145 cm tall and weighs 68 kg The 5 g medication is in a 0 5 L bag of 0 9 NS Calculate the rate in which you will set the pump 8 25

Integrate Oa 1 x 2x 5 3 C x 2x 5 2 x 2x 5 1 C Ob x 2x 5 x 1 dx C d x 2x 5 2 Od

10 Find the sum of the first 30 terms of the arithmetic sequence whose first term is 15 and whose common difference is 4

But we can rewrite the event on the LHS in terms of Tk and Tk 1 Since Tk is the sum of k independent exponentials of rate A we have Tk Gamma k and similarly Tk 1 Gamma k 1 X So P N 0 t k P Tk t Tk 1 t P Tk t P Tk 1 t 1 Ax k e x k 1 dx S Xx Xx ke x k dx 7 2

4 Consider the following equation y 3x 6x 24 a Write the equation in its related function form b Use the vertex formula to find the vertex c Solve the zero equation 3x 6x 24 0 Use the method of your choice d Graph the function Plot and label x and y intercepts the vertex and any other relevant points e State the axis of symmetry f Is the graph concave up or concave down g Use interval notation to state the interval where the graph is increasing h Use interval notation to state the interval where the graph is decreasing i Calculate the discriminant Then based on the discriminant identify the number of real solution

Find value s of h and k such that A exists A 1 0 1 5 k 1 h 2 2

20 Determine all vectors v that are orthogonal to u 11 2

5 Determine if S x 1 x2 is linearly independent or dependent

Determine if S 4t t 5 t3 5 3t 3t 2t3 is a basis for P3

Find the distance between u 1 2 5 and v VE 3 0 1

3 Determine if W the set of all odd functions is a subspace HERENTH

9 Find the dimension for M3 2

4 Determine if S 1 1 1 2 2 2 3 3 3 is linearly independent or dependent

5 Determine if S 1 2 1 1 is a basis for R

15 Find the vector with the given length v 3 and in the direction of u 0 2 1 1

Determine if W the set of all vectors in R whose components are integers is a subspace

Find the angle between u 2 3 1 and v 3 2 0

19 Determine if u 0 3 4 and v 1 8 6 are orthogonal parallel or neit

18 Determine if u 4 3 and v are orthogonal parallel or neither

3 Find the Wronskian for x ex x ex

Determine if W the set of all vectors in R2 whose second component is the square of the first is a subspac

d 3 points What is the inverse of 19281207 in mod 19381 You may leave your final answer with an exponent

Make or buy A company manufactures various sized plastic bottles for its medicinal product The manufacturing cost for small bottles is 55 per unit 100 bottles including fixed costs of 12 per unit A proposal is offered to purchase small bottles from an outside source for 36 per unit plus 3 per unit for freight a Prepare a differential analysis dated January 25 to determine whether the company should make Alternative 1 or buy Alternative 2 the bottles assuming fixed costs are unaffected by the decision If an amount is zero enter 0 Unit costs Differential Analysis Make Bottles Alt 1 or Buy Bottles Alt 2 January 25 Purchase price Freight Variable costs Fixed factory overhead Total unit costs Make Buy Differential Effects Bottles Bottles Alternative 1 Alternative 2 Alternative 2 X QOOQ

Product J19 is produced for 11 per gallon Product J19 can be sold without additional processing for 18 p gallon or processed further into Product R33 at an additional cost of 7 per gallon Product R33 can be sold 24 per gallon a Prepare a differential analysis dated April 30 on whether to sell Product J19 Alternative 1 or process further into Product R33 Alternative 2 If required use a minus sign to indicate a loss Differential Analysis Sell Product J19 Alt 1 or Process Further into Product R33 Alt 2 April 30 Revenues per unit Costs per unit Profit Closs ne Sell Product J19 Alternative 1 18 11 Process Further into Product R33 Alternative 2 24 18 Differential Effects Alternative 2 X X

A TI 84 calculator costs 110 18 Find the total cost of the calculator if sales tax is 8 Round to the nearest cent 1 118 99 2 117 71 3 100 27

2 Is growth by 60 every minute exponential or lincar 3 Is growth by 20 every week exponential or linear 4 Is decays by every day exponential or lincar 5 Is decreases by 8 inches every day exponential or lincar

7 Mechanical engineering technicians were number of years of experience and their current salary The data is shown below Years of Experience a 1 2 2 5 b 6 Salary 6 8 c 27800 44500 34300 37800 51175 53500 58200 Create a scatter plot of this data Use GoogleDocs Sheets to create the scatter plot 2 marks Equation of Line of Best Fit e Complete a linear regression and state the equation of the line of best fit and the R2 value 2 marks R R correlation coefficient According to the correlation coefficient what type of correlation what shape exists with this data What is the STRENGTH AND DIRECTION of the 2 marks relationship Use the equation in b to determine the salary of someone with 4 years 2 marks experience SHOW YOUR WORK

3 Lisa Carr purchases a truck 55200 and plans to pay for the vehicle through the dealership s financing plan She makes monthly payments on this balance for 5 years and the financing rate is 5 20 compounded monthly What will Lisa s monthly payments need to be to pay off her balance in 5 years 3 marks FOR SIMPLE INTEREST I pxrxt Annuities FUTURE VALUE OF AN ANNUITY 1 1 For COMPOUND INTEREST A P 1 i PRESENT VALUE OF AN ANNUITY PV R 1 1 1

Draw a valid conclusion from the given premises He was told that he had to shape up or ship out He didn t shape up Therefore Click the icon to view tables of standard valid and invalid forms of arguments Which conclusion is valid O He didn t have to ship out O He had to ship out O He shaped up None of the above

Katie wants to create a rectangular frame for a picture She has 60 inches of material If she wants the length to be 3 more than 2 times the width what is the largest possible length Write an equation and solve O6w 6 60 21 2w 3 4 60 15 A 6w 6 60 9 4 2w 3 60 6

Suppose that for a certain exam a teacher grades on a curve 24 2 2 0 1 13 6 13 6 30 20 lo fl lo 20 3 It is known that the mean is 65 and the standard deviation is 10 There are 45 students in the clas Frequency 34 1 34 1 What score would be necessary to obtain an A hovo 2 2 0 1

A daredevil wants to jump over a canyon on his motorcycle He travels approximately 88 ft sec at an angle of 30 when the motorcycle leaves the ramp at the edge of the canyon Choose a coordinate system with the origin at the end of the take off ramp and assume he lands at the same height a Write parametric equations to define the path of the motorcycle as a function of the time t in sec after leaving the ramp b If a bird is at a position 99 27 at a time 1 3 sec after the motorcycle leaves the ramp will the motorcycle hit the bird Assume a 1 ft margin of error

1 Solve the following IVPs Show the details a y sinh x cosy y 0 4 b c d xy y 3x cos y x xy 4y 8x4 y y y y 1 n 3 y 1 2 y 0 1 3

Coca Cola Enterprises CCE is the largest bottler of Coca Cola in Western Europe The company purchases Coke and Sprite concentrate from The Coca Cola Company KO dilutes and mixes the concentrate with carbonated water and then fills the blended beverage into cans or plastic two liter bottles Assume that the estimated production for Coke and Sprite two liter bottles at the Wakefield UK bottling plant is as follows for the month of May Coke Sprite In addition assume that the concentrate costs 75 per pound for both Coke and Sprite and is used at a rate of 0 15 pound per 100 liters of carbonated water in blending Coke and 0 10 pound per 100 liters of carbonated water in blending Sprite Assume that two liters of carbonated water are used for each two liter bottle of finished product Assume further that two liter bottles cost 0 08 per bottle and carbonated water costs 0 06 per liter Prepare a direct materials purchases budget for May assuming inventories are ignored because there are no changes between beginning and ending inventories for concentrate bottles and carbonated water 153 000 two liter bottles 86 500 two liter bottles Materials required for production Coke Sprite Feedback Coca Cola Enterprises Wakefield Plant Direct Materials Purchases Budget For the Month Ending May 31 assumed data Concentrate 2 Liter Bottles Total materials Direct materials unit price Total direct materials to be purchased Check My Work x s 459 lbs 173 632 lbs 75 153 000 btls 86 500 239 500 btls 0 08 Carbonated Water x 5 306 000 Itrs 173 000 479 000 Itrs 0 06 19 140 X

Situation II Water flows through a pipe at 130 L s that changes gradually in diameter from 154 mm at point A to 429 mm at point B Point B is 4 6 m higher than point A The pressures at point A and point B are 70 kPa and 48 3 kPa respectively Assume that the datum line passes through point A 8 Which of the following most nearly gives the specific energy at point A a 9 565 m c 6 979 m d 6 894 m b 9 618 m 9 Which of the following most nearly gives the specific energy at point B a 9 565 m c 6 979 m b 9 618 m d 6 894 m 10 Which of the following most nearly gives the head loss in the pipe a 0 053 m c 2 586 m b 0 085 m d 2 724 m

For which quadrant s is cosine positive Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4

30 gal y s 11 25 5 alatz 3 x 12 13 30 ta y s sat 4 25 30 13 12 lata y s sat galata y s sat galata alatt 3x 2 ss gal galata y s sat galata y s sat gal

Find the mean for the data items in the given frequency distribution Score x Frequency f 1 2 2 5 3 6 4 4 5 6 The mean is Round to 3 decimal places as needed 6 65 5 7 2 8 2

Find the derivative of the function Simplify and express the answer using positive exponents only c x 4x x 9 c x

se Newton s method to find all the roots of the following function Use preliminary analysis and graphing to determine good initial approximation f x 8 cos x 2 x 0 the root s is are x Round to five decimal places as needed Use a comma to separate aneware se pooded