Linear Algebra Questions and Answers

R 60 Find the indicated angle 80 120 120 P

K M The following angle can be described as Select

Consider the information about the economy of Pakistan Note that the currency of Pakistan is the rupee The government purchases 2 70 trillions of rupees Individuals consume 8 30 trillions of rupees Individuals save 4 92 trillions of rupees Businesses invest 1 35 trillions of rupees Foreigners spend 0 65 trillions of rupees to purchase Pakistani firms Pakistan imports 2 46 trillions of rupees Pakistan exports 1 38 trillions of rupees Calculate Pakistan s GDP Assume that the values are all current and no conversions need to be made Give your answer in terms of trillions of rupees and round to two decimals Pakistan s GDP 14 68 trillions of rupees

George works at a warehouse installing electronic devices on gas meters He receives a base pay of 200 and 35 cents for every electronic device installed Last week his pay was 437 65 How many electronic devices did he install Round to the nearest whole number if necessary xa 571 devices b 679 devices c 153 devices d 1 250 devices

The given vectors form a basis for R Apply the Gram Schmidt Process to obtain an orthogonal basis Use the Gram Schmidt Process found here to calculate your answer 0 0 0 X3 V3 V x2 V X 2 x2 X 4 4 4 0 3 3 2 2 2 X Normalize the basis V V V3 to obtain an orthonormal basis Enter sqrt n for n

Use a tree to model the parent child relationships in the following family Patty has three children Shelly Lulu and Kevin Shelly has one child Donna Lulu has two children Harpo and Bertie Kevin has no children Use vertices to model the people and edges to represent the parent child relationships Label the vertices with the person s initial Choose the graph that represents the parent child relationships O A L H B D S B Ke L S COL HBD O C K H L B D S O D Ka L HBD

Suppose the economy is in equilibrium and assume no government or foreign sector If total saving equals 90100 then intended investment must equal Your Answer

Assume f x f x 3 x 4 a x b 4 Find the following 2 T 1 KU

Extend 3 x 3 x to a basis for P Enter your answers as a comma separated list 2 x 3 x x x X

Find a basis for the row space of A 1403 A 1 1 1 4 0 3 1 3 1 6 1 2 1 1 111 36 21 Find a basis for the null space of A Verify that every vector in row A is orthogonal to every vector in na

Find the orthogonal decomposition of v with respect to the subspace W That is write v as w u with w in W and u in W 4 W U X 4 3 4 3 8 7 2 3 W span

Find an orthogonal basis for R4 that contains the following vectors 4 1 4 1 0 0 1 and 1 0 1 2 1 5 0 5 1 5 2 1

Extend 3 x 3 x x2 to a basis for P Enter your answers as a comma separated list 2

Extend 3 x 3 x x to a basis for P2 Enter your answers as a comma separated list x 3 x 3 x x x x 3 2

Determine the number of 5 card hands that have at least one club in them For the toolbar press ALT F10 PC or ALT FN F10 Mac R

3 of 12 A calculator may be used for this item The table shows the gross domestic product of the United States in billions of dollars at the start of each year since 1999 Part A Of the four one year intervals provided in the drop down list the one year interval where the average rate of change is the greatest is A B 2005 2006 C D 2000 2001 Part B 2010 2011 2015 2016 The average rate of change from 2013 to 2018 is billions of dollars 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 9631 10252 10582 10938 11458 12214 13037 13815 14452 14713 14449 14992 15543 16197 16785 17522 18219 18707 19485 20494

Let T P R be the linear transformation defined by T a bx cx cx 2 6 a Which if any of the following polynomials are in ker T Select all that apply 01 x O x x 1 x x none of these b Which if any of the following vectors are in range T Select all that apply 0 P 9 1 O

Let B and C be bases for R2 where C PC B 1 1 Let B Find the following vectors 41 c 4 4 8 Find B 3 B 31 and the change of basis matrix from B to C is

Consider the following 1 12 A 1 B 1 1 1 1 1 0 38 Let a and b be scalars Find aA bB aA bB Determine whether C is in span A B OC is in span A B OC is not in span A B

Consider the following 560 A 6 5 8 Los 5 Find all eigenvalues of the matrix A Enter your answers as a comma separated list 15 5 5 Give bases for each of the corresponding eigenspaces smallest value span largest 2 value span D Q span 3 4 5 4 1 4 3 0 1 3 4 5 4 Orthogonally diagonalize the matrix below by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ D Enter each matrix in the form row 1 row 2 wher separated list 1

A man has 235 000 invested in three properties One earns 12 one 10 and one 8 His annual income from the properties is 22 500 and the amount invested at 8 is twice that invest 12 a How much is invested in each property 12 property 10 property 8 property b What is the annual income from each property 12 property 10 property 8 property

Define linear transformations S P P and T P2 P by S a bx a a b x 5bx and T a bx cx b 5cx Compute S o T 8 5x x2 and S o T a bx cx 5 25x So T a bx cx b b 5c x 25bcx So T 8 5x x X Can you compute To S a bx If so compute it If an answer does not exist enter DNE To S a bx a b 25bx

Which proves that x 2 is a factor of the given polynomial function f x x 3 2x 2 x 2

Itranscript m likes to day trade on the Internet On a good day he averages a 1200 gain On a bad day he averages a 800 loss Suppose that he has good ays 20 of the time bad days 50 of the time and the rest of the time he breaks even What is the expected value for one day of Jim s day ading hobby nswer 2 Points Keypa Keyboard Shortc

The following table shows the number of cell phone subscriptions in a country in billions for selected years x after 200 2005 2006 2007 2009 9 4 X y 2008 a Find a function C x that models the data where x is years after 2005 b Predict the number of cell phone subscriptions in 2012 OA 2010 9 8 a Select the correct choice below and fill in the answer boxes within your choice Round to two decimal places as needed The best model for the data is a logistic function and is given by f x 1 OB The best model for the data is an exponential function and is given by f x The best model for the data is a logarithmic function and is given by f x www X X In x

2 Simplify without a calculator Show your work a 2 2 b 3 2 c 10 10 d

Can you solve the riddle In reply to an inquiry about the animals on his farm the farmer says I only ever keep sheep goats and horses In fact at the moment they sheep bar three all goats bar four and all horses bar five How are all many does he have of each animal

6 1 point State the range of f x 3x 4 a b v Ry Ry c d ye Ry 0 ye Rly 0

A medical prescription company was testing a new medication to prevent seizures They collected data on a person s weight and the amount of medication in his her bloodstream What type of data was collecte Bivariate and Quantitative Bivariate and Categorical

A Farmer measured the heights of his apple trees He recorded the results below Estimate the average height of his apple trees Show your wor 2 Frequexy 12 19 I N 70 75 80 85 90 Height feet For the toolbar press ALT F10 PC or ALT FN F10 Mac BIUS Paragraph V Arial Q TT 65 V 10pt BAEXE 111 28 83 E3 16 TO A I

What type of variability occurs with no human intervention or error

Solve the system of equations by graphing 2x y 5 x 2y 10 Use the graphing tool to graph the two equations 6 8 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution is Type an ordered pair OB There are infinitely many solutions OC There is no solution CH 10

10 10 Pts Find the mass of the 3D object with density function f x y z x y gm cm in the region D in the first octant where z 4 x y

Test the set of matrices for linear independence in M22 If it is linearly dependent express one of the matrices as a linear combination of the others 1 0 1 3 A B C D 3 3 1 1 7 17 3 121 12 10 2 X

Find a QR factorization of the matrix Enter sqrt n for n 0 3 57 105 30 Q R 0 0 707 0 707 1 414 0 C 1 0 816 0 40 0 408 2 12 3 67 0 577 0 577 0 577 3 53 2 014

Find a symmetric 2 x 2 matrix with eigenvalues 2 and 22 and corresponding orthogonal eigenvectors v and v M C 3 V2 A 1 A 8 V

Consider the transformation T M22 M22 defined by T A AB where B ker T 2 Find basis for the kernel of the linear transformation T Enter your answers as a comma separated list Enter each matrix in the form row 1 row 2 where each row is a comma separate 5 1 2 X Find either the nullity or the rank of T and then use the Rank Theorem to find the other nullity T 1 rank T 1

Consider the following V M22 B 4 Complete the following statements The elements of set Bare The set B has 3 Therefore the set Bis linearly independent X elements and dim M22 4 a basis for V

Consider the following A 500 0 D13 Find all eigenvalues of the matrix A Enter your answers as a comma separated list largest 2 value Give bases for each of the corresponding eigenspaces smallest A value span 0 3 1 span span Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ D Enter each matrix in the form row 1 row 2 where each row is a list 100

Find a QR factorization of the matrix Enter sqrt n for n Q 035 105 1 3 0 000 000 000

Select the true statement s about the graph of f x There is an asymptote at x 2 There is an asymptote at y 1 There is an x intercept at 4 There is an x intercept at 2 x 16 x 2

S 4x 9 toros of hare h x 4x 9 Use the drop down menus to factor the expression and find the zeros of h 3 and

1 HAO 0 3 3 1 5 9 Find the product of the first two matrices Select the correct choice below and if necessary fill in the answer box to complete your choice 3 1 0 3 5 9 OB The product is not possible Find the complete product Select the correct choice below and if necessary fill in the answer box to complete your choice A OA 4 1 0 3 3 1 3 1 4 860 3 1 5 9 2 OB The product is not possible

13 What is the pseudoinverse of 300 A 0 2 0 001

An assembly line machine turns out washers with the following thicknesses in millimeters Find the mean and standard deviation of the thicknesses 1 51 1 78 1 92 2 05 1 84 1 35 1 88 1 63 1 83 1 76 1 27 1 24 2 07 1 98 1 24 1 52 The mean is 1 6794 mm Round to four decimal places as needed The standard deviation is mm Use the answer for the mean to find this answer Round to four decimal places as needed

the following matrix if possible 0 8 Diagonalize 8 10

Goodman s budgeted overhead at normal capacity of 30 000 direct labor hours is 6 per hour variable and 4 per hour fixed In June 310 000 of overhead was incurred in working 31 500 hours when 32 000 standard hours were allowed The overhead controllable variance is

S Here is a square and some regular octagons In this pattern all of the angles inside the octagons have the same measure The shape in the center is a square Find the measure of one of the angles inside one of the octagons

escribe the point of view that occurs in The Occurrence at Owl Creek Bridge The point of view is third person limited and in the first part focuses objectively on the actions of the characters rather than their thoughts but as Farquhar gets closer to death the reader shares his final thoughts At first the point of view is omniscient and focuses on the thoughts of the soldiers who are about to kill this man but as Farquhar gets closer to death the point of view switches to first person and the reader shares his final thoughts At first the point of view is first person and focuses on Farquhar s feelings about death but as Farquhar gets closer to death the point of view switches to third person limited and focuses on the final preparations of the soldiers

ote that surface area is the total area of the surface of three dimensional object For example the surface area of a cube the area of all 6 faces added together ind the surface area of the prism he surface area of the prism is in L 7 in 3 in 6 in