Linear Algebra Questions and Answers

a recreation area are filling a small pond with water They are adding water at a rate of 30 liters per minute There are 500 liters in the pond to start Let W represent the amount of water in the pond in liters and let T represent the number of minutes that water has been added Write an equation relating W to T and then graph your equation using the axes below Equation 800 B 700 600 500 400 300 200 100 0 0 X X Espa E E IST

This question points possible Juan has 5 ties 6 shirts and 4 pairs of pants How many different outfits can he wear if he chooses one tie one shirt and one pair of pants for each outfit There are different outfits Juan can wear if he chooses one tie one shirt and one pair of pants for each outfit Type a whole number

Graph the numbers in the group on the number line Then write the numbers from largest to smallest 2 1 3 3 2 Graph the point 1 Graph the point 3 5 4 4 Graph the point 3 0 0 0

Work out the units for weight using W mg

3 Use a theorem covered in class to find a bound for the number of iterations needed to achieve an approximation with accuracy 10 3 to the solution of x 4 0 lying in the interval 1 4 Find an approximation to the root with this degree of accuracy using Bisection method code covered in class How many iteration did you need

K A plant manager is considering investing in a new 40 000 machine Use of the new machine is expected to generate a cash flow of about 9 000 per year for each of the next five years However the cash flo is uncertain and the manager estimates that the actual cash flow will be normally distributed with a mean of 9 000 and a standard deviation of 400 The discount rate is set at 5 and assumed to remain constant over the next five years The company evaluates capital investments using net present value How risky is this investment Develop and run a simulation model to answer this question using 50 trials Click the icon to view a sample of 50 simulation trial results 89 65 1 579 93 174 45 717 02 784 65 3 057 49 1 786 30 1 781 27 1 180 61 Say the values of the mean of the cash flow distribution the standard deviation of the cash flow distribution the initial investment and the discount rate are entered in cells B3 B4 B5 and B6 respectively The for the Monte Carlo simulation the cash flow for an individual year is randomly generated using the Excel formula NORM INV RAND B3 B4 If the randomly generated cash flows for the five years are i cells B9 C9 D9 E9 and F9 then the Excel formula for the net present value is B 5 NPV B6 B9 F 9 Type whole numbers Determine the risk level of the investment using the provided sample of 50 simulation trial results The probability of a nonpositive net present value is P NPV 0 This means the investment is Round to two decimal places as needed Simulation Results 2 604 18 901 40 2 344 31 685 61 1 899 89 1 205 22 3 069 45 1 195 65 774 76 68 69 913 51 1 552 81 1 966 66 1 827 60 1 261 51 131 44 695 02 827 36 253 69 954 05 714 76 942 82 818 66 413 88 960 97 1 228 96 133 11 2 041 97 1 349 45 458 31 14 83 697 51 1 071 15 1 512 50 264 67 1 708 99 XX X not very risky less than 25 chance of a negative NPV somewhat risky between 25 and 49 chance of a negative NPV quite risky between 50 and 75 chance of a negative NPV very risky greater than 75 chance of a negative NPV

Les From RAND 512121 D 60349 90587 98976 90709 03255 72195 64581 33869 24012 55275 52995 32305 77762 0757 36128 1003 1497 3364 9215 8453 4967 2598 4753 6489 X hoving product has the accompanying probability mass function Use VLOOKUP to generate 25 random variates from this distribution Click here to view the probability mass function Click here to view 25 random values Set up an Excel worksheet with the Demand x column of the probability mass function in column A and the Probability f x column of the probability mass function in column B Construct an F x column column for the cumulative probability function in column C an Interval Lower Bound column a column for the lower bound of the interval for each row in column D and an Interval Upper Bound column column for the upper bound of the interval for each row in column E Duplicate the Demand x column from column A in column F Construct a Random Number column a column with random numbers generated by RAND in column G and an Outcome column in column H Place all row headers in row 1 and place the Demand x categories 0 1 2 3 and 4 or more in cells A2 A3 A4 A5 and respectively Then for a worksheet set up in this fashion the appropriate VLOOKUP function for cell H2 using the appropriate random number generated in column G would be VLOOKUP s 3 Probability Mass Function Demand x 0 1 2 3 4 or more Probability f x 0 2 0 4 0 3 0 1 0 www X

Find the orthogonal decomposition of v with respect to W D projw v perpw v 3 W span 000 00

Find the orthogonal projection of v onto the subspace W spanned by the vectors u You may assume that the vectors u are orthogonal L u 11 O 5 C 0 ON

Alex plans to invest 5 000 for 8 years at State Bank that offers an annual rate of 4 8 compounded continuously How much interest is earned by the end of the 8 years 2 340 73 5 000 00 7 340 73 8 213 00 Question 5 18 points Which investment would be worth the most after 15 years An initial investment of 5000 compounded semi annually at a rate of 6 after 15 years An initial investment of 5000 compounded quarterly at a rate of 5 9 after 15 years 6500

POINT POINTS THE STANI 5 FOR THE DATA 63 A MEAN B MEDIAN 76 88 75 82

Determine if the given vectors form an orthogonal set ANA 6 36

Consider the following matrix A v v 3 2 1 2 Y 1 2 3 2 Find the inverse using the orthogonality 2 A

A square matrix A is invertible if and only if det A 0 Use the theorem above to find all values of k for which A is invertible k A 8 k k 0 k 1 15 5 1 k 1

Find all of the eigenvalues of the matrix A separated list 32 A 3 50

Classify if possible the critical point of the given plane autonomous system as a stable node a stable spiral point an unstable spiral point an unstable node or a saddle point x 1 5xy y 5xy y x y X Conclusion stable node

work 2 Anumeha mows lawns She charges an initial fee and a constant i The variable models Anumeha s fee in dollars for working t hours f 6 12t What is Anumeha s initial fee 3 Shyria read a 481 page long book cover to cover in a single session at a constant rate After reading for 1 5 hours she had 403 pages left to read How fast was Shyria reading How long did it take her to read the entire book 4 The pressure at sea level is 1 atmosphere and increases at a constant rate as depth increases When Sydney dives to a depth of 23 meters the pressure around her is 3 3 atmospheres The pressure p in atmospheres is a function of X the depth in meters Write the function s formula

A nurse hangs a 1000 milliliter IV bag which is set to drip at 125 milliliters per hour Create a model of this situation to represent the amount of IV solution left in the bag after x hours Itranscript Step 2 of 3 The slope is equal to the rate that the IV solution is the dispensed per hour What is the slope Hint consider whether the amount of IV solution in the bag is increasing or decreasing and how this would affect the slope Answer 2 Points Keypad Keyboard Shortcuts

The area of Trapezoid CDEF is 175 squara centimeters Find the area of Triangle CDF C 14 cm 11 cm

ns Jotform PhysioTech Question 14 of 26 View Policies Show Attempt History CD 0

The mass of a bag of kitty litte Choose the correct answer b O O 17 g 17 kg 17 mg

on 14 1 Homework K The preference ballots BCA ABC ABC ABC CBA A BCA CBA B CBA

orthland nts DETAILS ing calculator is recommended raphing device to graph the hyperbola y 10 W Assignment 12 Conic 15 1 5 y 10 5 A 10F y 10 5 M Speech 5 Submit Outl X 10 y 10 5 10 5 5 5 10H y Mail Salad Mo 10

1 Points DETAILS Find an equation for the conic whose graph is shown y 15 10 5 7 6 X

2 Recall the absolute value of a R defined by al a a In lecture we proved the triangle inequality a 20 a 0 a b a b a beR a Review the proof of the triangle inequality as long as you need to until you can write it down without looking at your notes b Show that the triangle inequality can be written as la b a b a b R c Show that b a a b a d Show that b a a b a e Prove the reverse triangle inequality ab la b a b R f Prove a b c a b c for a b c ER by applying the triangle inequality twice Hence for n EN numbers a 02 an use induction to prove

1 Let S be a non empty subset of R that is bounded above a Prove that sup S is unique In other words if s and s2 are both the lowest upp bounds of S then s 82 b Suppose sup S belongs to S Prove that sup S max S

Let A 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 a Solve the least squares problem Ax b where b P Note that the columns of A are orthonormal why 48 b Find the projection matrix P that projects vectors in R onto R A Ax c Compute Ax and Pb Pb B 2

Find the partial fraction decomposition for each rational function 9x 23 x 1 x 7 13x 2 90x 25 2x 3 50x 8x 13 x 2 x 1

Consider the following matrix A v v 1 2 1 2 A Q 1 2 1 2 Find the following dot products V V V V Determine whether the given matrix is orthogonal The matrix is orthogonal O The matrix is not orthogonal Find its inverse Enter sqrt n for n If it not orthogonal enter NA in any single blank

Show that A and B are not similar matrices 21 3 4 B 5 6 p 2 A 6 Since A has characteristic polynomial p 2 1 the two matrices are not similar and B has characteristic polynomial

Determine if the given vectors form an orthogonal set GOD O These vectors form an orthogonal set O These vectors do not form an orthogonal set

Compute the determinant using cofactor expansion along the first row and along the first column 105 2 1 1 0 1 3

Nicole runs a large animal shelter The Amador family adopted a puppy named Birdie from the shelter When Birdie was adopted she had been at the shelter for 78 days At Nicole s shelter the length of stay for puppies has a mean of 91 days and a standard deviation of 12 days a Find the z score of Birdie s length of stay at the shelter relative to the the lengths of stay for all the puppies at the shelter Round your answer to two decimal places 0 b Fill in the blanks to interpret the z score of Birdie s length of stay at the shelter Make sure to express your answer in terms of a positive number of standard deviations Birdie s length of stay was standard deviations Choose one the mean length of stay for all the shelter above below X DI

ve using artificial variables e maximum is z when x X1 and X2 Maximize subject to with z 3x 2x x x 70 X1 4x 2x 150 5x 2x2 250 x 0 X 20

sembly line machine turns out 1 83 1 97 1 38 1 81 1 88 1 57 2 02 1 51

Question list O Question 5 Question 6 O Question 7 1

Use the like bases prope 1 3 x 5 3 7x 10

how Transcribed Text Write the given pression in

The following function is positive and negative on the given interval 5x f x sin 2x a Sketch the function on the given interval b Approximate the net area bounded by the graph of f and the x axis on the interval using a left right and midpoint Riemann sum with n 4 5x C Use the sketch in part a to show which intervals of 2x make positive and negative contributions to the net area a Choose the correct answer below OA OB AY 1 0 1 2x NEW 30 5 1 1 tot st www Q o 27 OC 1 0 1 tot st 3 2 2 O G D 1 10 24 FH for 2 2 O 0

161 The graph of y YA 2 1 0 1 24 1 2 x f t dt where f is a piecewise constant function is shown here 3 4 5 6 x a Over which intervals is f positive Over which intervals is it negative Over which intervals if any is it equal to zero b What are the maximum and minimum values of f c What is the average value of f

For each equation determine whether it is linear Equation a x 6xy 3 b 4 31 X 5 2 3y 1 c 3y 9 d 6x 9 5y y 8 Is the equation linear Yes No O

Use the function to find the image of v and the preimage of w V T V V V V V V V 7 2 w 7 17 a the image of v b the preimage of w If the vector has an infinite number of solutions give your answer in terms of the parameter

The inverse forms of the results in Problem 49 in Exercises 7 1 are s a 6 52 2 1 and eat cos bt b 1 8 33 6 eat sin bt s a Use the Laplace transform and these inverses to solve the given initial value problem y y e 5t cos 4t y 0 0 y t

Suppose A is a Hermitian positive definite matrix Show that there is a UNIQUE Hermitian positive definite matrix B such that B

1 Determine the points of intersection between the linear equation f x 1 5x 5 and g x 2x 12x 13

Find the least squares solution of the system TE 2 P T 1 1 1 1 1 1 1 1 7 5 9 5

Determine whether the given matrix is orthogonal 3 2 1 2 3 2 2 Q The matrix is orthogonal O The matrix is not orthogonal Q Find its inverse Enter sqrt n for n If it not orthogonal enter NA in any single blank 1 2 sqrt 3 2 S sqrt 3 2 1 2

What is the sum of all values of m that 19 satisfy 2m 9m 9m 11 0 00 00 00

a stronger correlation r 0 722 or r 0 893 Explain your reasoning Choose the correct answer below A r 0 722 represents a stronger correlation because 0 722 0 893 B r 0 722 represents a stronger correlation because 0 893 0 722 OC r 0 893 represents a stronger correlation because 0 893 0 722 OD r 0 893 represents a stronger correlation because 0 722 0 893

Write down the first 6 square numbers Work out these squares and square roots 14 2 49 144 3 43 1 1 1 1 d p 1 Write down the first 6 cube numbers Work out these cubes and cube roots 2 27 3 343 1 1 1 1