Matrices & Determinants Questions and Answers

Espa An initial amount of 3100 is invested in an account at an interest rate of 9 per year compounded continuously Assuming that no withdrawals are made find the amount in the account after five years Do not round any intermediate computations and round your answer to the nearest cent

Use the following preference schedule to answer questions 44 and 45 6 4 C B D A First choice Second choice Third choice Fourth choice 5 D C B A 8 A D C B A C 44 Which candidate will be chosen if the Contingent Method is used A A B B C C D D 45 Which candidate will be chosen if the Instant Runoff Method is used A A B B C C

cide whether or not the equation has a circle as its graph If it does give the center d the radius If it does not describe the graph x y 8x 4y 4 elect the correct choice below and if necessary fill in the answer boxes to complete your choice DA The graph of the equation is a point OB The graph of the equation is a line OC The graph of the equation is a circle with center The radius of the circle is OD The graph is nonexistent Type an ordered pair

Using the 68 95 99 7 Rule determine what of values lie in the space marked with X 3 s d O 0 15 2 35 13 5 34 X 2 s d 1 s d mean 1 s d 2 s d 3 s d

The predicted temperature for the next 10 days in Fahrenheit is the following 71 75 74 80 83 86 90 85 81 80 What is the median temperature in Fahrenheit Do not round your answer

Consider the double jointed robotic arm shown in the figure Let the lower arm be modeled by a 2 1 2 the middle arm be modeled by b 3 4 3 and the upper arm by c 2 3 4 where units are in feet a Find a vector d that represents the position of the hand b Determine the distance of the hand from the origin a d 0 0 0

Given v 9j and w j a find the dot product v w b find the angle between v and w c state whether the vectors are parallel orthogonal or neither a v w b What is the angle betweenv and w Do not round until the final answer Then round to the nearest tenth as needed c Are vectors v and w parallel orthogonal or neither O orthogonal Oparallel

Vials in a chemistry lab are marked with letters Each vial is filled with a chemical In the table below an X denotes the pairs of chemicals that cannot be mixed together AB C D E F A X X X X B X X X C D X X X X E X X F X X X In making a graph to represent these conflicts how many edges would be on vial B

3 S 0 02 Rx d 5 is S in 1 You must support your answer C1 C ER a 12 points Find a 3 x 4 reduced echelon matrix R and a vector d E R such that the solution set of the linear system 1 b 5 points Suppose that the augmented matrix R d of the linear system Rx d that you determined in part a in reduced echelon form is obtained from the augmented matrix A b of another linear system Ax b by first subtracting 3 times the first row from the second row then subtracting 5 times the second row from the third row Find the 3 x 4 matrix A and the vector b E R Show the details of your work c 8 points Now consider any linear system Cx f for some 4 x 4 matrix C and vector fER whose solution set is S in 1 Is the set consisting of columns of C linearly independent Why or why not

a 13 points Find a 4 x 4 matrix C such that i C is not invertible and ii every entry of C is nonzero b 12 points Does there exist a 5x2 matrix A and a 2x5 matrix B such that AB is invert Either provide a 5x2 matrix A and a 2x5 matrix B such that AB is invertible or other show that for every 5x2 matrix A and every 2x5 matrix B the product AB is not invert

Find the orthogonal projection of b 4 4 2 onto the column space of the matrix A Enter each vector as a comma separated list of its components A 4 2 2 0 1 4 2 4 1

1 pt Let v W WI 3 and u 2 For W span u write vias the sum of two orthogonal vectors w in Wland win W

1 pt Perform the Gram Schmidt process on the following sequence of vectors in the given order then normalize the resulting orthogonal basis 8 6 0 y I 2

9 Find the volume between the cone x Spherical coordinates y z2 and the sphere centered at 0 0 0 of radius 2 U

Find the following indefinite integral 3x2 1 x Xdx O a x x c C b x x ex c d C 4 14 3x

whether the system is inconsistent or the equations are dependent 3x 3y 3z 3 4x 2y 9z 25 2x 4y 3z 3

Use the figure to answer the questions below 00 Given that the circle has a radius of 8 express the area of the figure highlighted in blue in the image as a function of 0 Assume that is measured in rac A 8

st tive terms of the recursively define sequence a n 1 3a n 5

5 Find the third derivative of f x 4sinx a f x 600 b f x 60 4 c f x 600 7 X 4cosx 60 4cosx 4cosx

For mutually exclusive events R R and R we have P R 0 05 P R 0 7 and P R 0 25 Also P Q R 0 7 P Q1R 0 5 and P Q1R 0 2 Finc P R 10 P R 19 Type an integer or a simplified traction

Find the multiplier for 11 8 growth 11 8 1 118 88 2 0 882

Jse synthetic division to find the quotient and remainder when 8x a Complete this synthetic division table 2 8 21 U 3 0 20 21x x 2 1 b Write your answer in the following form Quotient 20 1 x 2 21x 20 is divided by x 2 by completing the parts belo Remainder x 2 X

4 Compute the SVD of the matrix 1 1 2 2 1 1 2 2

Find an orthogonal matrix Q that diagonalizes S e 4 Gl 1 31 FI G What is A

4 Compute the SVD of the matrix 1 1 2 1 2 2 1 2

The given matrix determines a linear transformation T Find all x such that T x 0 4 2 6 3 5 9 0 9 6 14 6 4 9 1 7 7 Select the correct choice below and fill in the answer box within your choice OA There is only one vector which is x OB X XA C X X D x x X3 XA

Find a possible formula for the polynomial shown on the right The black point labelled on the graph is 1 4 NOTE Enter the formula with lowest possible degree y 60 50 40 30 20 10 10 10 20 30 40

ork Homework 7 2 list K Toward the middle peaches for cannin late and extra late date of ripening D to the right were re

asis for the column space of A is vector A L 3 2 1 5 6 27 9 10 15 8 3 12 1 00

Give integers p and q such that Nul A is a subspace of RP and Col A is a subspace of R 0 A 7 16 5 06 7 4 3 2 2 Nul A is a subspace of RP for p and Col A is a subspace of R for q

Find the nullspace 1 4 1 8 A 0 2 of A 2 1 4 1 1 2

nd the inverse of the matrix A A ex ex ex ex ex e ex e x

Which of the following tables represent functions A B E F X y X y X y X y X y X 1 5 1 8 6 1 4 5 5 5 9 10 1 1 8 10 11 20 1 4 3 10 6 6 6 2 3 4 11 13 22 13 9 5 11 2 18 5 13 15 26 15 6 5 12 12 2 3 15 30 14 20 100 107 160

Use the graph to approximate the number of points of intersection of the graphs of y and Y2 Y 2 sin x 23x 1 3x N KIN 2 3 point s of intersection y 3 2 y KIN Y 2 3x 2 X

H Select all of the vectors that are in the span of u u Check every statement that is correct Let U G A The vector B The vector and 12 is in the span D All vectors in R2 are in the span OG We cannot tell which vectors are in the span C The vector 8 E The vector 3 F The vector is in the span 6 3 is in the span is in the span is in the span

Next question gement of a firm wishes to check on the opinions of its workers Before the workers are interviewed they are divided into various categories Define events E F and G asa shown Complete parts a through f E Worker is on the day shift F Worker has worked more than 4 years G Worker contributes to a voluntary retirement plan c Describe the event EU G in words OA The worker is on the night shift and the worker contributes to a voluntary retirement plan OB The worker is on the day shift and the worker does not contribute to a voluntary retirement plan OC The worker is on the night shift or the worker contributes to a voluntary retirement plan or both OD The worker is on the day shift or the worker does not contribute to a voluntary retirement plan or both d Describe the event F in words The worker has worked for e Describe the event FUG in words OA The worker has worked for more than 4 years or the worker contributes to a voluntary retirement plan or both OB The worker has worked for less than 4 years or the worker does not contribute to a voluntary retirement plan or b Submit qu

S Use Cramer s rule to find the value of x that satisfies the system of linear equatic 5x y 2z 3 Sx 5y 3z 0 3x 4y z 1 1000 The determinant of the coefficient matrix is D 60 20

Graph the functions f x x g x x 5 and system Then describe what effect adding a constant parabola 10 9 bot 9 8 7 6

V1 V2 4 Let G be a basis for a vector space V of dimension m Show that a linear combination of vecto is equal tov in V if and only if there is a linear combination of the coordinate vecto V g V2 g Vk g that is equal to the coordinate vector v in R Vk

P find the change of coordinates matrix from the basis B 1 52 2 1 91 1 41 to the standard basis Then write t as a linear combination of the polynomials in B In P2 find the change of coordinates matrix from the basis B to the standard basis P C B Simplify your answer Write t as a linear combination of the polynomials in B P 5 2 1 01 1 41 Simplify your answers

ermine the number of solutions to the augme rix 0 0 4 3 103 1

termine the number of solutions to the augmented trix 201 1 1 ct one a 14 32 35 01 no solution b 1 solution c 2 solutions IN d infinitely many solutions

Let y 1 and u 3 Write y as the sum of a vector in Span u and a vector orthogonal to u y z Type an integer or simplified fraction for each matrix element List the terms in the same order as they appear in the original list

Question 14 Find the common ratio and wri

2 Show Transcribed Text O X M M F 1 M 3 1 V 2 y 1 2 y 1

Draw a picture of T house for these matrices D 3 and A 7 7 3 3 and U H 0 1

Let p 1 x2x p2 4 4x 8x p3 7 Find a basis for the subspace of P2 spanned by the given vectors If less than 3 vectors are required one or more of the vectors below can be set to zero Use the above vectors if possible I e use v37 instead of v3 1 V1 V V

Use the definition of Ax to write the vector equation as a matrix equation 2 5 0 4 Z 23 Z4 2 8 8 Z 0 14 0 4

Let W be the subspace spanned by the given vectors Find a basis for W B W W 0 5

Consider the following 4 05 6 16 5 04 a Compute the characteristic polynomial of A det A 2 2 A b Compute the eigenvalues and bases of the corresponding eigenspaces of A Repeated eigenvalues should be entered repeatedly with the same eigenspaces 2 N 23 li has eigenspace span has eigenspace span has eigenspace span 1 11 11 c Compute the algebraic and geometric multiplicity of each eigenvalue A has algebraic multiplicity and geometric multiplicity 22 has algebraic multiplicity and geometric multiplicity 23 has algebraic multiplicity and geometric multiplicity smallest value largest value