Basic Math Questions and Answers

Apply the alternative form of the Gram Schmidt orthonormalization process to find an orthonormal basis for the solution space of the homogeneous linear system U1 U2 x1 x2 2x3 3x4 0 2x1 x2 4x3 6x4 0 x Show Transcribed Text x1 x2 2x3 3x4 0 2x1 x2 4x3 6x4 0 C Apply the alternative form of the Gram Schmidt orthonormalization process to find an orthonormal basis for the solution space of the homogeneous linear system

Do the given vectors form an orthogonal basis for R Yes the given set does form an orthogonal basis for R O No the given set does not form an orthogonal basis for R You are given the theorem below Let V V V be an orthogonal basis for a subspace W of R and let w be any vector in W Then the unique scalars c C such that W C V SKK are given by W V for i 1 k v V Use the theorem to express was a linear combination of the above basis vectors Give the coordinate vector w of w with respect to the basis B v V V of R w g V W 0 12 54 1 12

A matrix A is given along with an iterate xg 1 760 533 A a Compute the next iterate x X6 AX5 X5 7573 2293 Use these data to approximate a dominant eigenvector whose first component is 1 and a corresponding dominant eigenvalue Use three decimal place accu dominant eigenvector dominant eigenvalue 0 30278 5 13 2 7573 b Compare the approximate eigenvalue from part a with the actual dominant eigenvalue 1 Find the characteristic polynomial det A 2 22 52 3 Find the dominant eigenvalue 5 13 2 x

Consider the following A 3 02 a Compute the characteristic polynomial of A det A 21 23 32 92 5 b Compute the eigenvalues and bases of the corresponding eigenspaces of A Repeated eigenvalues should be entered repeatedly with the same eigenspaces A 1 03 2 1 d 5 has eigenspace span has eigenspace span has eigenspace span 0 1 0 41 1 1 41 1 4 3 1 c Compute the algebraic and geometric multiplicity of each eigenvalue 7 has algebraic multiplicity 2 2 has algebraic multiplicity 2 and geometric multiplicity 2 and geometric multiplicity 2 smallest value largest value

A matrix A is given along with an iterate x 4 335 13 002 a Approximate the dominant eigenvalue and eigenvector by computing the corresponding m and y Round your answers to three decimal places mk 13 002 A Yk 1 0 333 b Verify that you have approximated an eigenvalue and an eigenvector of A by comparing Ay with my Round your answers to three decimal places AV k myk X 4 332 12 999 4 329 13 002

The following facts can be proven 1 An orthogonal 2 x 2 matrix must have the form where 2 Every orthogonal 2 x 2 matrix is of the form or is a unit vector 2 sin 0 cos 0 2 3 or where 0 0 2m 3 An orthogonal 2 x 2 matrix Q corresponds to a rotation in R if det Q 1 and a reflection in R2 if det Q 1 sin 0 cos 0 Use the above facts to determine whether the given orthogonal matrix represents a rotation or a reflection Orotation O reflection If it is a rotation give the angle of rotation If it is a reflection give the line of reflection Enter the angle if it is a rotation Enter an equation involving x and y if it is

Consider the following orthogonal set of vectors v Find the following values v v3 V V4 1 2 1 2 1 2 1 2 11 6 3 1 6 6 V3 3 2 3 6 3 6 3 6 V4 Determine whether the given orthogonal set of vectors is orthonormal O The set is orthonormal O The set is not orthonormal 0 1 2 2

Consider the following orthogonal set of vectors v V Find the following values v 1 2 1 2 1 2 Determine whether the given orthogonal set of vectors is orthonormal O The set is orthonormal O The set is not orthonormal

Determine whether the given matrix is orthogonal 1 1 5 1 Q Q 1 4 1 4 1 2 1 2 0 5 2 5 O The matrix is orthogonal O The matrix is not orthogonal Find its inverse If it is not orthogonal enter NA in any single blank

Jogging A highschool truck is an Oval that measure 400m around If Savamah jogs around the track Six times how many kilometers has she gone

Find the dot product of each pair of the given vectors 1 0 V V V V3 V V3 V V4 E V V4 11 V3 V4 11 V V 0 1 2 1 Determine if the given vectors form an orthogonal set O These vectors form an orthogonal set O These vectors do not form an orthogonal set 0 1

Consider the dynamical system x 1 AXk 0 3 0 3 0 3 A a Compute x X X3 for Xo x X3 b Compute x X X3 for Xo 8 X x 1 X3 00 c Using eigenvalues and eigenvectors classify the origin as an attractor repeller saddle point or n attractor O repeller O saddle point

P is the transition matrix of a regular Markov chain Find the long range transition matrix L of P 3 P 1 1 288 1 1 228 3 8 1 0 1 2

Write out the first six terms of the sequence defined by the recurrence relation with the given initial conditions Yo 0 y 7 Yn Yn 1 Yn 2 for n 2 Yo Y Y2 Y3 Y4 M Y5 11 11 11 11 11

Use the method of Example 4 29 to compute the indicated power of the matrix 0 2000 0 1999 5 2 0 7999 0 8000 6

Name integrated Math 5 Describe a composition of transformations that maps JKLM to PQRS 6 Given AACD and AABE what is AB 7 Given APQR and ASTU what is meQe 8 For what value of x is AABC ADEF 9 What additional information would prove AJKLAXYZ 14 42 4 In 12 O 21 P Q K J 2 28 46 Unit 5 Mini GPA 1 S R A 8 7x 10 E 9 115 D 12 56 6 M 70 94 4x 6

Sketch each curve in the z plane and sketch its image under w a z1 1 b x 1 c y 1 e y r 1 x 0 f y 1 1 1 0 d y x 1

7 Fix p 0 p 1 and fix zo z1 E C Show that the set of z satisfying and p 2 with z zol plz z is a circle Sketch it for p zo 0 and 21 1 What happens when p 1

Determine angles a b and c shown in the Figure 1 The vertical lines are of course parallel 75 B FIGURE 1 Problem 2 Determine length ED for the similar triangles shown in Figure 2 S a KIN C D C CO W F 16 D

4 Let T be the set of all the rooted trees on the vertex set n with the root 1 How many trees in T have exactly 2 leaves In this question we assume n 3

6 For fixed a C show that za 11 z 1 if z 1 a 1 z 0

Suppose that AABC is right angled at B and has AB n n 1 and AC n 1 n 4 where n is a positive integer Determine the number of positive integers n 100 000 for which the length of side BC is also an integer

Question 14 8 Part 1 of 2 g tower was originally 185 5 feet high At a distan is found to be 64 Find ZRPQ indicated in the f

B 40 C 60 b 8 A Simplify your answer a Type an integer or decimal rounded to two decimal places as needed C Type an integer or decimal rounded to two decimal places as needed

Sum and difference identities Problem type 3 Use the information given below to find sin a B sin a tan 3 5 12 with a in quadrant II 5 with B in quadrant III Give the exact answer not a decimal approximation sin a B 010

ne 22784 n 7 2 Qu Find the slope of the line passing through

G Find the slope of the line passing throug points rises falls is horizontal or is vert

Graph the function f Then use the horizontal line test to determine whether the inverse of f is a function f x x OYes the function passes the horizontal line test Yes the function passes the vertical line test No the function does not pass the horizontal line test No the function does not pass the vertical line test

Your answer is incorrect Use a sum or difference formula to find the exact value of the following 7 15 tan 1 tan 3 tan 7 15 5 55 5 TC tan T 1 X VE

TRIGONOMETRIC IDENTITIES AND EQUATIONS Sum and difference identities Problem type 2 Radians Use a sum or difference formula to find the exact value of the following 7 15 tan tan TC 5 7 TU 5 1 tan tan 15 8 9

Consider the following 0 11 a Compute the characteristic polynomial of A det A Z 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 5 50 0 23 has eigenspace span has eigenspace span has eigenspace span 11 c Compute the algebraic and geometric multiplicity of each eigenvalue A has algebraic multiplicity and geometric multiplicity A has algebraic multiplicity and geometric multiplicity A has algebraic multiplicity and geometric multiplicity smallest value largest value

Find all of the eigenvalues of the matrix A Hint Use the method of Example 4 5 of finding the solutions to the equation 0 det A AI Enter your answers as a comma sep list 2 Give bases for each of the corresponding eigenspaces span A span smaller value largor ASK YOUR T

Let p P 5 12 1 3 1 4 0 N H be the transition matrix for a Markov chain with three states Find p 3 3 2 3 7 18 W NW H 1 3 5 18 0 What proportion of the stat 7 18 2 9 7 18 population will

a Sketch the graph of the parametric curve x 3 sint 3 y 4 cos t 0 t a y 4 2 4 y 2 Need Help 2 X 2 4 Read It 4 6 8 8 10 10 X X 2 y y 4 2 b Eliminate the parameter t in part a to obtain an equation for this curve in rectangular coordinates x 3 4 S 2 4 6 2 8 10 10 X

LS Window Help et in circular motion is modeled by the given parametric equations Describe the path the time t that it takes to complete one revolution around the circle 3 sin t 1 on

A pair of parametric equations is given x cos t y sin t 0 t 2 a Sketch the curve represented by the parametric equations y 1 5 1 0 0 5 1 5 1 0 0 5 1 5 1 0 6 5 0 5 1 0 1 5 1 5 1 0 0 5 0 5 y 1 0 1 5 0 5 0 5 1 0 1 5 x 1 0 1 5 X X 1 5 1 0 1 5 1 0 b Find a rectangular coordinate equation for the curve by eliminating the parameter x y x cos 1 y sin 1 0 5 0 5 0 5 1 0 0 5 1 0 1 5 1 5 1 5 0 5 0 5 1 0 1 0 1 5 y y webassign net 0 5 0 5 1 0 1 5 1 0 1 5 X

A pair of parametric equations is given x cos 2t y sin 2t a Sketch the curve represented by the parametric equations y X 1 Need Help 3 3 2 1 x 0 Read It 1 X 3 2 2 y 3 2 WERS 1 2 WebAssign Plot 2 3 b Find a rectangular coordinate equation for the curve by eliminating the parameter 2 3 X X 3 f 1 3 2 1 1 1 1 3 1 y y 1 2 3 3 X

Consider the function g x sin xt dt a Fresnel integral which is given in terms of a definite integral and a variabile upper limit a Graph the integrand b Calculate g x c Graph g a Choose the correct graph below TAA M OD

A flight travels daily from Pittsburgh to San Antonio The following list gives the flight s arrival time in minutes relative to the scheduled arrival time for a selection of 8 days A negative number means the flight arrived that many minutes early 35 27 27 35 8 24 5 4 Send data to calculator a What is the mean of this data set If your answer is not an integer round your answer to one decimal place 0 0 b What is the median of this data set If your answer is not an integer round your answer to one decimal place c How many modes does the data set have and what are their values Indicate the number of modes by clicking in the appropriate circle and then indicate the value s of the mode s if applicable 0 5 Ozero modes Oone mode 0 O two modes and

A B C estion 10 ct the statement below that is FALSE es

ion 8 statement is TRUE about the relationship between a includes that journal

h answer below correctly completes this sentence works cited page u must list the information for each source in the order that follows MLA guideline u can list the information for each source in any order as long as you include the re ormation should list only the information that you think your audience needs to find your s e URL is all you need to include

518519 quizzes 3952985 take Question 3 How does the works cited for both a print bo Author s last name first name

Question 9 What which of the following items are considere A Publisher B Publication date C Title of container D Author E All of the above F None of the above

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Brianna deposited 95 000 in an investment fund that was growing at a rate of 3 00 compounded quarterly for a period of 5 years and 9 months a What is the accumulated value of the investment at the end of 5 years and 9 months Round to the nearest cent b What is the amount of interest earned from this investment

Find the amount of money in an account after 13 years if 7000 is deposited at 7 annual interest compounded a follows a Annually b Semiannually c Quarterly d Daily Use n 365 e Continuously a The account will contain 16 868 92 after 13 years when the interest is compounded annually Simplify your answer Type an integer or decimal rounded to two decimal places as needed b The account will contain after 13 years when the interest is compounded semiannually Simplify your answer Type an integer or decimal rounded to two decimal places as needed

Is the function described in the table below concave up or concave down X g x 0 10000 5 9000 Concave up Concave down 10 7000 15 4000 20 0

Use the plot plan shown in the figure below to answer the problem Answer to the nearest cubic yard t How much gravel is necessary if it is to be laid to a depth of 6 inches Assume a 120 b 84 and c 18 yd3 75 60 Section A 155 b Blue Represents Building Lawn Section B Gravel c d Section C 60 240 415 Fountain base Second Street 90 SII Reflecting pond

on Find the average rate of change of f x x 2 x or the interval 1 9 Average rate of change