Differential equation

1. Write a short paragraph comparing and contrasting the method of undetermined coefficients and variation of parameters. How are they similar, how they are different? If you had your choice, which method would you use? 2. Consider the differential equation: my"+cy'+ky=mg+sqrt(t) Why would the method of undetermined coefficients be difficult to use for this problem?

Observational / Variable Units of Interest; Population / Process of Interest; Null / Alternative Hypothesis

*Please see attachment for case study. Questions: (a) What are the observational units and variable units of interest in this study? Also specify the population or process of interest. (b) State and nell and an alternative hypothesis about the value of pi (in words and symbols) (c) We can assess the strength of evidence against the null hypothesis by treating 897 current atheletes as a random sample from the process of athlete determination at Brown. If we initially give the university the benefit of the doubt and assume the nully hypothesis is true, does the Central Limit Theorem for a sample proportion apply here? Explain.

Eigenvalues and Eigenspaces

Find the eigenvalues and their multiplicities for the following: (see attachment) Also, find a basis of eigenvectors for each eigenspace and identify any deficient eigenspace.

linear independence

Determine whether or not the three vectors listed above are linearly independent or linearly dependent. **they are linearly independent*** The vectors were written horizontally this time, as they often are in books, but that is just to save space. The problem is the same as if the vectors were written vertically. If they are linearly dependent, determine a non-trivial linear relation - (a non-trivial relation is three numbers which are not all three zero.) otherwise, if the vectors are linearly independent, enter 0's for the coefficients, since that relationship always holds (please see attached for full question)

linear dependence

The vectors (see attached) are linearly independent if and only if k does not equal ____?