Matrices & Determinants Questions and Answers

Let S be the solid obtained by rotating the region shown in the figure about the y axis Assume a 3 and b 2 YA 3 0 Sketch a typical approximating shell y y ax x b 2 00 8 4 2 2 X 3 X 2 2 1 y 1 1 2 X

The price p in dollars of a specific car that is x years old is modeled by the function below p x 22 295 0 90 a How much should a 5 year old car cost b How much should a 6 year old car cost c Explain the meaning of the base 0 90 in this problem a A 5 year old car should cost approximately Round to the nearest whole number as needed

Graph the solution set If there is no solution indicate that the solution set is the empty set y 1 3 x 4 y x 2

Suppose each of three construction industries dwellings construction roads and bridges construction and public and private businesses construction requires the following input in order to produce one dollar in output 3 1 The dwellings construction industry requires nothing from itself of a dollar from roads and bridges construction and of a dollar from public and private 10 3 businesses construction 1 The roads and bridges construction industry requires of a dollar from dwellings construction none from itself and of a dollar from public and private 1 3 businesses construction The public and private businesses construction industry requires of a dollar from dwellings construction of a dollar from roads and bridges construction 1 4 3 8 and none from itself Suppose further that the total production capacity of the dwellings construction industry is 300 of roads and bridges construction is 360 and of public and private businesses construction is 240 Find the external demand that can be met using the total production capacity of the system Write the exact answer Do not round ver from dwellings construction from roads and bridges construction Keypad Keyboard Shortcuts Tables

ppose that in a certain local economy we have aircraft boat automobile and computer industries Given the following input output matrix determine which industr most dependent on the aircraft industry Assume that the rows and columns of the matrix follow the above order of industries swer A Aircraft 0 1 0 2 0 0 6 None are dependent on Aircraft O All are equally dependent on Aircraft O Computer O Automobile O Boat 0 5 0 2 0 0 3 0 3 0 4 0 0 2 0 1 0 1 0 2 0 2 Keypa Keyboard Shortc Tables

XI 8 x3 Given the following input output matrix A and corresponding demand matrix E for a local economy find the production matrix X where X answer Do not round Answer k 0 1 0 3 0 3 A 0 1 0 3 0 1 0 5 0 1 0 3 XI x2 E 600 400 500 x2 Write the exac Tables Ke Keyboard Sh

Suppose that in a certain local economy we have natural gas and coal industries To produce one dollar in output each industry needs the following input The natural gas industry requires 0 2 from itself and 0 3 from coal The coal industry requires 0 8 from natural gas and 0 1 from itself all a12 Find the input output matrix A of this economic system where A Assume the first row and column correspond to the natural gas industry and the a21 a22 second row and column correspond to the coal industry Write the exact answer Do not round Answer all a12 a21 Keypad Keyboard Shortcuts m Tables

Apply the eigenvalue method to find a general solution of the given system Find the particular solution corresponding to the given initial values Use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system x 3x 4x x2 3x 2x2 x 0 x 0 1 COCCOD The eigenvalue s of the constant coefficient matrix is are Use a comma to separate answers as needed Simplify your answer Type an exact answer using radicals and i as needed

8 2 Find tan a B exactly given sin a and sin 8 where a terminates in quadrant IV and B 5 terminates in quadrant IV Be sure to reduce your final result completely

Verify each identity 20 points 1 21 2 cot x 1 tan xcos x

Determine the particular solution of the ODE system below when f t and g t 0 x 2 0 X 0 C D 2 g t

et P 3 2 3 1 3 4 0 V 6 1 5 2 2 U 6 4 and v 3 8 4 Complete parts a and b 5 a Find a basis u U U3 for R such that P is the change of coordinates matrix from u u u to the basis V V V3 H What do the columns of P represent C B

Apply the Gram Schmidt orthonormalization process to transform the given basis for R into an orthonormal basis Use the vectors in the order in which they are given B 4 3 1 0 U U

the equation below by Pst s lecting the correct function Sine Curve or Cosine Curve and then using the draggable points Provide your answer below ATT Note to view the values of points on the graph click on the line You will see grey dots at maximums minimums intercepts and inflection points Use maximums minimums and the y intercept to check your answer 4 3 2 1 N 1 Sine Curve 2 Cosine Curve 2TT y cos x 37 JT 47 2

Evaluate the expression 6x5y 2x4 y for the following values of x and y x y Value of Expression 1 19 2 1 36 14 3 1 23

Determine whether the relation defines y as a function of x Give the do y x 5 11

Sketch the region and then find the centroid of the region O Show Transcribed Text

Find A B Enter the element in row 1 column 2 A 2 3 1 5 B 1 3 2 4

n your answers show all your calculations When solving a system of linear equations you m irstly form the augmented matrix and solve the matrix by using row reductions Show all yo eductions step by step Answers that are written directly without the proper solution steps a alculations will be given partial or no credit 3 Let T be a linear operator on a finite dimensional vector space with a matrix representation 2 0 0 A 12 6 4 6 2 01 a Find the eigenvectors of A Find the dimension of each eigenspace of A b Using the result of a explain why the operator T is diagonalizable c Find a matrix P and diagonal matrix D such that D P AP d Find two other matrices P and P and corresponding diagonal matrices D and D such that D P AP and D P AP2

1 point Consider a triangle ABC for which ZA 110 a 28 b 10 f such a triangle can not exist then write NONE in each answer box If there could be more than one such triangle then enter dimensions for the one with the smallest value for side c Finally if there is a unique triangle ABC then enter its dimensions ZB is degrees C is degrees

Use the inverse of the matrix in Exercise 5 to solve he system VIEW 2y z 2 2x 4y z 1 2x y 2z 5

In a clinical study of niacin as a lipid altering agent 60 of the 90 patients in the study group developed flushing Calculate the number of patients having this reaction Round to a whole number

V The reduced row echelon form of a system of linear equations is given Write the system of equations corresponding to the given matrix Une x y and as variables Determine whether the system is consistent or inconsistent If it is consistent give the solution 10 8 01 00 5 6 0 0 C What equation does the first row represent Type an equation What equation does the second row represent Type an equation What equation does the third row represent Type an equation Determine whether the system is consistent or inconsistent If it is consistent give the solution Select the correct choice below and if necessary fill in the answer box es within your choice OA The system is consistent The solution is 1 1 Simplify your answers OB There are infinitely many solutions The solution can be written as x y z x y z is any real number Simplify your answers Type expressions using z as the variable OC There are infinitely many solutions The solution can be written as x y z x y is any real number z is any real number Simplify your answer Type an expression using y and z as the variables D The system is inconsistent

1 95 5 8 3 Which of the following is the system of equations corresponding to the augmented matrix O A O C x 9y 3 5x 8y 5 8x 9y 5 5x y 3 Perform the row operation What is the resultant matrix OB O D x 5y 5 9x 8y 3 x 9y 5 5x 8y 3

Question 5 The percent of women in the U S civilian labor force can be model fairly well by the function 67 21 1 1 081e x 24 71 f x where x represents the number of years since 1950 a What percent to the nearest whole number of U S women were in the civilian labor force in 2015 Show work Answer b In what year were 56 of U S women in the civilian labor force Show work

If B is the standard basis of the space P3 of polynomials then let B 1 1 12 13 Use coordinate vectors to test the linea independence of the set of polynomials below Explain your work 1 21 1 1 41 1 1 21 Write the coordinate vector for the polynomial 1 21 1

Solve the matrix equation Ax b where 9 61 1 x 9 A The solution is x1 4 x2 4 6 and b 66 36

Construct A so that N A all multiples of 4 3 2 1 Its rank is Give answer with all steps

4 x 4 matrix A with rows v v2 v3 and v4 has determinant det A 9 en det V1 5v2 4v3 5v2 9v3

5 75 points For the bases below a find the transition matrix from B to B b find the transition matrix from B to B and c verify that the two transition matrices are inverses of each other B 1 0 1 1 and B 1 1 1 1

Assume that A is row equivalent to B Find bases for Nul A Col A and Row A 13 4 2 5 1 3 0 25 26 3 79 39 069 A B 130 2 6 004 4 4 000 0 8 0 0 0 0 A column vector basis for Nul A is Use a comma to separate vectors as needed A column vector basis for Col A is Use a comma to separate vectors as needed A row vector basis for Row A is 0

Solve the system and write the solution as a vector A 2 4 1 5 L 2 4 3 1 0 b 2 2 9

1 If C 1 x y 1 X y Calculate det 3C x y

Find the matrix product 27 5 2 24 5 0 1 O of O 5 14 8 6 O 4 16 10 4 O 01 5 O 5 14 8 8 5 12 8 8 5 14 8 8 1 1 3

j 2 k 3 4 Let v 4 and V In addition the vector b 0 is given Consider the plane Li 2k 2 V Span V V Calculate the shortest distance from b to V Hint Find the projection of b onto V 5 k 9

What does the solution of the following system of linear equations represen geometrically 2 1 0 1 1 0 Two non intersecting planes Two lines intersecting at a point Two planes intersecting at a line Three planes intersecting at a point Neither of listed here 7 2 3 0 0

Find the area of the region cut from the first quadrant by the curve r 10 3 sin 20 A WAREN DET HELYER ARTE FUEN Type an exact answer using it as needed 7 2 1

1 Find a minimum value for the radius of convergence of a power series solution about a 0 to z 3 z 16 y 2 a 5 y z 1 y 0

find a onit in the vector in the direction of the vector 18 30 40

Write the definition of the Cartesian product A x B of sets A B d prove that that RX Q R

A couple bought some stock for 20 per share that pays an annual dividend of 1 20 per share After 2 years the price of the stock was a What is the return on investment 16 X b Find the simple interest rate on the growth of their investment 5 I X

Marchetta Bakery sells three kinds of cookies pignoli snickerdoodle and macaroon Re investing in the business Marchetta Bakery has been able to open four additional locations and it is still growing A table showing the income from each kind of fudge per location is given below There are five locations Middletown Newark North Middletown Egg Harbor City and Savannah Marchetta Bakery Income Statement for the Year Ended December 1 2021 Location Pignoli Snickerdoodle Macaroon Middletown Newark North Middletown Egg Harbor City Savannah 120 million 150 million 184 million 172 million 172 million 108 million 184 million 127 million 141 million 220 million 78 million 94 million 82 million 101 million 99 million Source Bake Weekly Issue 196 July 1 2022 Marchetta Bakery plans to use 45 of its income from the sales of pignoli cookies 29 of its income from the sales of snickerdoodles and 26 of its income from the sales of macaroons when investing in creating its next location Write a matrix product that gives the amount to be used for investment at the end of the year 2021 16 144

on 2 Marchetta Bakery must select a supplier for the ingredients that it uses in two of its New Jersey locations Middletown and Newark Each location uses different amounts of ingredients The different unit amounts of these ingredients are shown in a table Location Middletown NJ Fine Sugar Fine Sugar Brown Sugar 22 Confectioner s Sugar 15 Brown Sugar Sonny Bones Obtuse Brix 131 251 168 274 16 12 Confectioner s Sugar Newark NJ Source Bakers Weekly Issue 196 July 1 2023 The two supply companies being considered Sonny Bones Obtuse Brix and Charlie Boy Massecuite can each supply all these ingredients but at different prices per unit as described in the table below 142 19 Charlie Boy Massecuite 173 156 11 143 Honey 13 12 Honey Source Bakers Weekly Issue 196 July 1 2022 Use matrix multiplication to decide which supplier should be chosen to supply a 1 the Newark location

Marchetta Bakery uses fine sugar brown sugar confectioner s sugar and honey The purchase prices and delivery costs per unit for these ingredients are displayed in the table below Marchetta Bakery Supply Charges Fine Sugar 10 Confectioner s Sugar 55 71 Purchase Brown Sugar 41 Delivery 25 33 Source Bakers Weekly Issue 196 July 1 2022 Create matrix M to represent the table of unit costs If the supplier announces a 21 increase on both purchase and delivery of these ingredients find the new unit cost matrix Honey 72 28 Refer to Chapter 3 1 Example 7 of our text for guidance Use Excel or Google Sheets Write the cost matrix M then use a scalar multiplier much like the one used in this example of our text and write out the calculation showing the new unit cost matrix as the result Write a short paragraph explaining how the new costs were calculated

c f x VA is are HA is OA is 4x 4x 24 x 3x 10 X y y

A 25 ft ladder is leaning against a house when its base starts to slide away By the time the base is 7 ft from the house the base is moving away at the rate of 24 ft sec a What is the rate of change of the height of the top of the ladder b At what rate is the area of the triangle formed by the ladder wall and ground changing then c At what rate is the angle between the ladder and the ground changing then a The rate of change of the height of the top of the ladder is Simplify your answer b The area is changing at Simplify your answer c The angle is changing at ft sec rad sec ft sec y t 0 25 ft ladder x 1

football is in the shape of a prolate spheroid which is simply a solid obtained by rotating an ellipse 8 25 inches in center circumference if the volume of a prolate spheroid iszab how much air does that football contain Neglect material thickness The football contains approximately of ar 1 about its major axis A football is 10 105 inches in len CETTA

You are given E 0 1x 1x 2x T True or False It is possible to find 7 The value of T B 77 1 1 2x 2 1 T 3 8 x 5 x 7 x T 0 1 x 1 x 1x

4 You are given 7 2 2 T23 i True or False it is possible to find T i The value of T 31 F

Type your answers in all of the blanks and submit X X 2 Use the functions to answer each question Enter infinity or infinity as needed Do not insert blank spaces in your answers f x 7 and g x 7 20 40 a To obtain the graph of g shift the graph of f Write your response here units and Write your response here up down b Domain of g in interval notation c Range of g in interval notation d Equation of horizontal asymptote Type your answer here Write your response here Write your response here left right Type your answer here Write your response here units