Linear Algebra Questions and Answers

tudent PlayerHomework aspx homeworkId 64382 ews Translate mework Ques The letters x and y represent rectangular coordinate x 10y

The table below lists the height h in cm the age a in years the gender g 1 Male 0 Female and the weight w C kg of some college students We wish to fit a linear function of the form Height Age Gender Weight 163 22 63 165 19 64 179 19 87 180 21 88 172 20 80 CI C2 0 f t co chc a c39 to these data Find the best approximation of this form using least squares CO 0 1 1 1

Find the equation of the circle determined by the given conditions Illustrate and show complete solution Passes through the points a 1 4 1 0 and 2 1 b 1 2 5 4 and 10 5

SUDmit Assignment Tes Question 6 of Trying to prepare a his electric bill and these bills each mo

Estimate the solution to the following system of linear equations by performing the first three Jacobi iterations Use an initial guess of 0 0 0 T C1 11 4x12x2 x3 32 1 1 7x3 17 63 3x1 8x2 2x3

Determine if the following function is a polyn 3 2 f x x 3x 8 Select the correct choice below and if necessary fill in the answer box to complete your choice O It is a polynomial The degree of the polynomial is OIt is not a polynomial

4 points Consider a vibrating system described by the initial value problem x t 4x t 4x t 50 cos 2t satisfying 0 0 and z 0 0 i Solve the initial value problem Answer x t ii Determine the steady state part of the solution ie the solution as t Answer t iii Which of the following is the correct parametric plot of a t a t Draw a sequence of values as increases taking x t along the horizontal axis and x t along the vertical axis to find the correct result O B C

Suppose that y varies directly wit a Write a direct variation Equation n

1 Pt 3 1 2 3 X 4 B 2 0 1 2 3 1 2 3 c 9 Y S 1 z 5 4 y y x 1 X Hol 0 Identify the y intercept b Find the slope Rate of Change of the line Write the equation of the line in 1 2 3 1 O O I Y 2 y mx b me XO 24 0 1 2 x 0 9 2 3 40 2 x 3 Se ruh 3 y x Y 0 1 2 3 y 2x 9 X 0 1 2 3 Y 9 1 13 15

a b c d Ope p v o p p v Ot 1 2 o t 1 2 04 3 4 5 5 04 3 5 6 O 9 11 13 o 9 11 13 1 3 5 7 1 3 5 7

Select the three models that represent a factor pair of the number 12

A shipment of 8 computers contains 3 with defects Find the probability that a sample of size 4 drawn from the 8 will not contain a defective computer

When a constant force acts upon an object the acceleration of the object varies inversely with its mass When a certain constant force acts upon an object wit mass 4 kg the acceleration of the object is 13 m s If the same force acts upon another object whose mass is 26 kg what is this object s acceleration 2 m s DO

2 E 7 4 F 2 3 G 0 7 H 9 8

Policies ent Attempt in Progress lumber Corporation reported 720 culate the profit margin and 8

15 Solve the nonlinear plane autonomous system by changing to polar coordinates Describe the geometric behavior of the solution that satisfies the given initial conditions s x x y x y y y x x y X 0 1 1

9 4 15 Find the general solution to the system X 1 25 X 5

1 10 Write the linear system X system of scalar equations 31 x Sint without using matrices That is write it as a set or

8 15 a Convert the second order nonlinear differential equation 2x xx x into a two by two autonomous system b Find all critical points of the resulting system

MY NOTES PRACTICE ANOTHER A sinking fund is established to discharge a debt of 30 000 in 25 years If deposits are made at the end of each 6 month period and interest is paid at the rate of 4 compounded semiannually wh is the amount of each deposit Round your answer to the nearest cent

Use the simplex method to maximize the given function Assume all variables are nonnegative Maximize f 2x 7y subject to the following 2x 5y 30 x 5y 25 x ys 14 x y

Let T P P2 be defined by T ao ax a x 9ao 7a1 19a2 a 49a2 x ao 4a2 x Find the eigenvalues of T NOTE Enter any repeated eigenvalues as often as they repeat

A q y t z p as follows a Find the total number of proper subsets of A 0 b Find the total number of subsets of A 0

You are running correlation analysis on a data set with 8 items You calculate the correlation coefficient to be 0 973 What is the critical value Is there significant correlation Yes O No

Evaluate the determinant List the property used for each step Show all your work Ala 1 2 2 4 1 4 4 1 1 2 2 8 11 13 1 14

2 Use the function below to find the values X G x A G 2 5 0 1 2 3 4 LO 5 4 3 2 1 0 B G 4 C All x values for which G x 0

The total cost in dollars to produce q units of a good is given by the function C q 5 6q 41000 A What is the total cost to produce q 3200 units Total cost B What is the cost of the 3201st item 2201

2 91 Points vertex An equation of a hyperbola is given x y 16 25 a Find the vertices foci and asymptotes of the hyperbola E x y smaller x value vertex DETAILS focus 1 x y SALGTRIG4 12 3 012 x y larger x value smaller x value

se includes data from student evaluations of courses The summary statistics are n 94 x 3 43 s 0 67 Use a 0 10 significance level to test the claim that the population of student course evaluations has a mean equal to 3 50 Assume that a simple random sample has been selected Identify the null and alternative hypotheses test statistic P value and state the final conclusion that addresses the original claim What are the null and alternative hypotheses OA Ho 3 50 H H 3 50 OC Ho H 3 50 H H3 50 Determine the test statistic Round to two decimal places as needed Determine the P value Round to three decimal places as needed State the final conclusion that addresses the original claim Ho There is CTLE OB Ho H 3 50 H 3 50 O D Ho H 3 50 H 3 50 evidence to conclude that the mean of the population of student course evaluations is equal to 3 50 correct

Do the given vectors form an orthogonal basis for R O 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 are given by 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 V3 C W

Use the power method to approximate the dominant eigenvalue and eigenvector of A to two decimal place accuracy Choose any initial vector you like and apply the method until the digit in the second decimal place of the iterates ste changing A 10 1 6 050 115 dominant eigenvalue dominant eigenvector

Find the dot product of each pair of the given vectors 6 9 3 12 V V 11 V V3 V V3 V 2 6 2 7 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

Solve the recurrence relation with the given initial conditions Xo 0 x 4 x 2xn 1 3xn 2 for n 2 Xn

A is a 2 x 2 matrix with eigenvectors V Find A x 524293 512 524283 512 X 1 and v 1 co corresponding to eigenvalues and 2 respectively and x 3

A matrix A is given along with an iterate x5 68 931 34 344 A X5 a Compute the next iterate x X6 AX5 34 Use these data to approximate a dominant eigenvector whose first component is 1 and a corresponding dominant eigenvalue Use three decimal place accur dominant eigenvector dominant eigenvalue b Compare your approximate eigenvalue in part a with the actual dominant eigenvalue A Find the characteristic polynomial det A 2 Find the dominant eigenvalue

row A col A 3 1 1 Points 11 R 4 4 F 10 10 10 11 1 DH 1 DETAILS COH 01 1 Find a basis B for the span of the given vectors HOU 19 PREVIOUS ANSWERS POOLELINALG4 3 5 0

Consider the following 99 List the eigenvalues of A and bases of the corresponding eigenspaces Repeated eigenvalues should be entered repeatedly with the same eigenspaces smaller value 1 smaller value A Yes Determine whether A is diagonalizable O No 7 10 D P Xhas eigenspace span X has eigenspace span 0 0 Find an invertible matrix P and a diagonal matrix D such that P 1AP D Enter each matrix in the form row 1 row 2 where each row is a comma separated list If A is not diagonalizable enter N SOLUTION

A is a 2 x 2 matrix with eigenvectors V Find A x A x 3149724 16384 1958426 16384 X x and V corresponding to eigenvalues 1 2 13 and 2 respectively and x

a i T I The Complex Plane and Elementary Functions eSmil4 E i 2 c 1 i e m 2 The eight eighth roots of unity e 8 1 3 g 1 i 8

In general it is difficult to show that two matrices are similar However if two similar matrices are diagonalizable the task becomes easier In the exercise below show that A and B are similar by showing they are similar to the same diagonal matrix A 3 1 2 diagonal matrix for A diagonal matrix for B P B 1 1 6 Find an invertible matrix P such that P 1AP B

Consider the following 100 881 901 List the eigenvalues of A and bases of the corresponding eigenspaces Repeated eigenvalues should be entered repeatedly with the same eigenspaces A smallest A value largest value 2 Determine whether A is diagonalizable O Yes O No has eigenspace span has eigenspace span has eigenspace span 1 11 Find an invertible matrix P and a diagonal matrix D such that PAP D Enter each matrix in the form row 1 row 2 where each row is a comma separa SOLUTION OUR TEACH

A List the eigenvalues of A and bases of the corresponding eigenspaces Repeated eigenvalues should be entered repeatedly with the same eigenspaces smaller 2 value smaller value Determine whether A is diagonalizable Yes O No has eigenspace span has eigenspace span 11 11 Find an invertible matrix P and a diagonal matrix D such that P AP D Enter each matrix in the form row 1 row 2 where each row is a comma separated list If A is not diagonalizable enter NO SOLUTION D P

Consider the following 00 0014 0021 a Compute the characteristic polynomial of A det A 2 2 3 A b Compute the eigenvalues and bases of the corresponding eigenspaces of A Repeated eigenvalues should be entered repeatedly with the same eigenspaces dz has eigenspace span has eigenspace span has eigenspace span has eigenspace span 11 c Compute the algebraic and geometric multiplicity of each eigenvalue and geometric multiplicity and neomatric multiplicity 2 has algebraic multiplicity multiplicity smallest value largest 2 value

A diagonalization of the matrix A is given in the form P AP D List the eigenvalues of A and bases for the corresponding eigenspaces Repeated eigenvalues should be entered repeatedly with the same eigenspaces 2 1 2 1 1 14 1 2 3 7 14 14 1 1 2 3 7 4 3 3 317 1 0 001 1 1 332 L 6 has eigenspace span has eigenspace span 1 0 1 11 600 00 00 1 11 W 0 smallest value

Determine whether A is diagonalizable OYes O No A D P 404 044 440 Find an invertible matrix P and a diagonal matrix D such that P AP D Enter each matrix in the form row 1 row 2 where each row is a comma separated list If A is no SOLUTION

Compute the indicated power of the matrix 1 1 1 0 1 0 0 0 1 2015

Show that A and B are not similar matrices Enter your answers as comma separated lists 619 009 A 100 068 B 19 0 689 Since A has eigenvalues and B has the eigenvalues the two matrices are not similar Y

Consider the following 1 4 3 0 2 5 1 2 3 6 3 4 5 8 9 9 Solve the system Ax b using the given LU factorization of A by first solving Ly b for y y X A 0000 Use the above to solve the system 34 3 10 3 00 3 1 2 0 0 0 1 00 3 2 10 5 4 2 1 1 4 3 0 03 5 2 00 20 0 0 01 b 1 3 1 0

er is a larger whole that holds a source Which item is NOT a con se aper n 2 9 core elements of a works cited entry Does every type of sourc

Given x 15cm 28 Find the grey area Answer 51 27 Br B e a A