Verify that the three eigenvectors found for the two eigenvalues of the matrix in that example are linearly independent and find the components of the vector i = ( 1 , 0 , 0 ) in the basis consisting of them. Using

\begin{vmatrix}1 & 0 & 0 \\ -4 & 7 & 2 \\ 10 & -15 & -4\end{vmatrix}

Which of these is the answer?

(2,−5,2)(2,−5,2)

(−1,3,23)(−1,3,23)

(1,−3,32)(1,−3,32)

Solve the following differential equation using Linear operators and the Annihilator approach as needed.

y''+2y'+y=x^2-3x

Does {1,2,3} ,{3,4,5}, {1,4}, {1,5}, {2,4}, {2,5} form an incidence geometry? If so do any of the parallel postulates hold (Elliptic, Euclidean, Hyperbolic parallel postulates)?

Interpret the meaning of a loading function

I just need an exemple

Suppose that e(t) is a piecewise defined function

e (t) = 0 if 0 ≤ t < 3

and

e(t) = 1 if 3 ≤ t

Solve

y’’+ 9y = e(t)

y(0) = 1 y’(0) = 3

y=fx1, ……..,x5)

St:

c1=w1(x1, ……..,x5)

c2=w2(x1, ……..,x5)

By using the signs of the principal minors Hj

1-Derive the second- order-sufficient condition for maximum.

2-Derive the second order-sufficient condition for minimum

A round-robin tournament is an event wherein every competing team plays every other team once and only once. Assuming no ties, every game can be depicted on a graph G using a directed edge (x, y), where team x has defeated team y.

(a) Assuming n teams participate in a round-robin tournament, how many vertices and edges will graph G depicting the tournament have?

(b) Is it preferable to be a source or a sink in graph G?

(c) Can G have multiple sources and/or sinks? Explain why or why not.

(d) Assuming G has a cycle, can it have a sink? Explain why or why not.

a) 8t*dydt+y=t^3, t>0
Put the problem in standard form.
Then find the integrating factor, μ(t)=________

b) 5(sin(t)dydt+cos(t)y)=cos(t)sin6(t), for 0<t<π and y(π/2)=18.

Put the problem in standard form.

find y(t)=___________

c)   13(t+1)dydt−9y=36t, for t>−1 with y(0)=18
Put the problem in standard form.

find y(t)=_______

d) x^2−4xy+x*dydx=0

Put the problem in standard form.

Find the integrating factor, ρ(x)=

6. The function f(t) =

0 for − 2 ≤ t < −1

−1 for − 1 ≤ t < 0

0 for t = 0

1 for 0 ≤ t < 1

0 for 1 ≤ t ≤ 2

can be extended to be periodic of period 4. (a) Is the extended function even, odd, or neither? (b) Find the Fourier Series of the extended function.(Just write the final solution.)

A beam is embedded at the left end and free at the other end with a constant loadw0=48EI uniformly distributed across its length. (6pts)

and L =1.

(a)Is this an initial value problem? Explain.

(b) Write and solve the beam deflection equation. Find the deflection when L=1/2

The town of Ferndale has four candidates running for mayor: the town barber, Darrell; the fire chief, Clough;the grocer, Abel; and a homemaker, Belle. A poll of 1000 of the voters shows the following results:

DABC = 225

CABD = 190

CADB = 210

BADC = 375

Is there a winner using the plurality method?

1. D

2. A

3. B

4. C

The seniors at Weseltown High School are voting on where to go for their senior trip. They are deciding on Angel Falls(A), Bend Canyon(B), Cedar Lake(C), or Danger Gap(D). The results of the preferences are:

DABC = 120

ACBD = 100

BCAD = 90

CBDA = 80

CBAD = 45

Who wins using the Borda count method?

1. Danger Gap(D)

2. Bend Canyon(B)

3. Cedar Lake(C)

4. Angel Falls(A

Show that a subset of R is open if an only if it can be expressed as a union of open intervals

Find a singular value decomposition for the matrix A = [ 1 0 -1, -1 1 0] (that means 1 0 -1 is the first row and -1 1 0 is the second)

If you could provide a step-by-step tutorial on how to complete this I'd greatly appreciate it.

Curve-fitting Project - Linear Model

Instructions

For this assignment, collect data exhibiting a relatively linear trend, find the line of best fit, plot the data and the line, interpret the slope, and use the linear equation to make a prediction. Also, find r² (coefficient of determination) and r (correlation coefficient). Discuss your findings. Your topic may be that is related to sports, your work, a hobby, or something you find interesting. If you choose, you may use the suggestions described below.

A Linear Model Example and Technology Tips are provided in separate documents.

Tasks for Linear Regression Model (LR)

(LR-1) Describe your topic, provide your data, and cite your source. Collect at least 8 data points. Label appropriately.  (Highly recommended: Post this information in the Linear Model Project discussion as well as in your completed project. Include a brief informative description in the title of your posting. Each student must use different data.)

The idea with the discussion posting is two-fold: (1) To share your interesting project idea with your classmates, and (2) To give me a chance to give you a brief thumbs-up or thumbs-down about your proposed topic and data. Sometimes students get off on the wrong foot or misunderstand the intent of the project, and your posting provides an opportunity for some feedback. Remark: Students may choose similar topics, but must have different data sets. For example, several students may be interested in a particular Olympic sport, and that is fine, but they must collect different data, perhaps from different events or different gender.

(LR-2) Plot the points (x, y) to obtain a scatterplot. Use an appropriate scale on the horizontal and vertical axes and be sure to label carefully. Visually judge whether the data points exhibit a relatively linear trend. (If so, proceed. If not, try a different topic or data set.)

(LR-3) Find the line of best fit (regression line) and graph it on the scatterplot. State the equation of the line.

(LR-4) State the slope of the line of best fit. Carefully interpret the meaning of the slope in a sentence or two.

(LR-5) Find and state the value of r², the coefficient of determination, and r, the correlation coefficient. Discuss your findings in a few sentences. Is r positive or negative? Why? Is a line a good curve to fit to this data? Why or why not? Is the linear relationship very strong, moderately strong, weak, or nonexistent?

(LR-6) Choose a value of interest and use the line of best fit to make an estimate or prediction. Show calculation work.

(LR-7) Write a brief narrative of a paragraph or two. Summarize your findings and be sure to mention any aspect of the linear model project (topic, data, scatterplot, line, r, or estimate, etc.) that you found particularly important or interesting.

You may submit all of your project in one document or a combination of documents, which may consist of word processing documents or spreadsheets or scanned handwritten work, provided it is clearly labeled where each task can be found. Be sure to include your name. Projects are graded on the basis of completeness, correctness, ease in locating all of the checklist items, and strength of the narrative portions.

A sequence (xn) converges quadratically to x if there is some Q ∈ R such that |xn − x| ≤ Q/n^2

for all n ∈ N. Prove directly that if (xn) converges quadratically, then it is also Cauchy.